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11/24/03 Back on November 11, Eric Goldstein passed 100 million digits with the number 879!!!

11/6/03 I have been slow with the updates for these pages. But I've been slow with them in the past, and I'm sure there will be times in the future that I am slow with them. Sorry. It's just life... :-)

Berend Jan van der Zwaag of the Netherlands has brought to my attention that the palindromes and the quantities listed on the Dataset Info page is probably wrong. His testing showed different results than mine. I went back, and my initial tests show that he is correct. I seem to have made an error in my LabView app that was looking for those numbers... I'm TRYING to find the problem and get it corrected. I don't think there is anyone who is using those numbers for anything, but I bring it up, just in case...

Felipe Barone of Brazil has mentioned that there are references and ideas that we seem to have missed, located at http://www.cs.arizona.edu/icon/analyst/ia.htm. He cites articles 30 through 35, 37, 39, 40, 43, 45 through 51, and 57. It appears that Icon is a programming language, and the articles are geared specifically toward this language, but they are still worth a quick read... Even though they are aimed at applications written in Icon, it is well worth the time to read the articles, since they provide an array of ideas for math solutions and other thoughts about the questions on Lychrel numbers. It's also nice to see that the digit distribution they show in paper 31, is similar to the pairings I talked about back around October 2002.

10/19/03 I have spent most of the day reading, and re-reading all of the pages that make up this site. With the exception of the Blackboard Archive, I have gone through and made an attempt to modify and reword all of the other pages to match the terms defined on the new Definitions page. I'm SURE I missed some. If you notice something on another page that conflicts with what is there, trust the Definitions page first, and contact me to make the change. THANKS!!

Thanks to Jason for all of his "advanced features" web page help!!

10/18/03 LOTS and lots of changes here. Mostly the frame for navigating. I THINK it is working correctly. If you have any problems, please report them to me!!! I've tested with Opera and IE, and they seem to be O.K., but, I'm never confident till it's been worked over a while. :-) If anyone is linking to any page other than www.p196.org, I'd ask you to change it. That way, everyone comes in through the front door. I've noticed that the site seems to be just fine in Opera if entered from the index.html page, but if I just come in from a subpage, Opera hangs. IE seems to work fine, but not Opera. I guess it's JavaScript just ain't up to snuff.

Eric G. has managed to cut 2:31 from his deep time!! He said; ...I coded a neat trick to handle carries even better..." and ... now I use only MMX!... His new times put him back in front of Vaughn, and can be seen over on the Software Comparisons page.

Matt sent me a new app to test, but it lost time compared to his last one. I'm waiting to hear from him.

I've added a "Files, Files, Files" page. There probably isn't anything there that most people want, but I've got lots of odds and ends gathered in one spot. Some of the bigger files aren't actually there, but if you want them, let me know, and I'll send them to you directly. I expect this page to grow larger as I get things organized from this "move".

I've got a space holder set up for a "Definitions" page, but there are still a lot of them that need to get ironed out, so for right now, it is blank. I'll get them up as I feel confident that there is no debate going on over a particular word...

10/12/03 Matt has moved ahead of Chris Lomont for his newest app. He shaved over a minute off his shallow time, and almost 12 minutes off his deep test. Great Job Matt!!

Felipe Barone of Brazil has written an application testing the "Order of Magnitude" of palindromes, as I asked for on my Wish List page. He sent it to me this evening, and I currently have it running from 1 - 10 digits. I'm not sure how long it will take to complete that many digits, but we'll find out... I have it running to 125 iterations for each number that does not form a palindrome. Jason Doucette's recommendation of 3 times the current world record. seems more appropriate for what he's doing, but since he has shown that all numbers with 10 digits or less solve in 109 iterations or less, I figured 125 was a nice round number. (Unless I'm misunderstanding Jason's page!!)

Anyway... I got a couple of other interesting emails from Felipe today. One of his quotes: ...that lead me to an observation that i think you missed in your trivial insights: There are infinitely many Twin Palindromes! Or in other words: there are infinitely many numbers P such that P and P + 2 are palindromes! Just like its conjectured that there are infinitely many twin primes! isn't this exciting!!!

I observed that from the order analyzer results and as i stop to think ITS SOMEWHAT OBVIOUS: 99 and 101, 999 and 1001, and so on... I don't have a proof for this conjecture, yet. but its empirically true.

Some other examples might be 689, 691 and 1495, 1497. Although 691 is obviously a kin number of 196, and the other three are Kin numbers of something else. (It's late, I need to go to bed, and I can't think right now. Figure it out for yourself. :-) ) But it does some an interesting "pattern" as you scroll through the list of numbers...

I say again that I really like the fact that almost every time someone new comes to my pages and writes me, they make a statement or point out an observation that no one has ever pointed out before. Is the above note useful in proving Lychrel numbers will not solve? Probably not. But is it interesting in itself? My answer is yes!!

Then, in a follow up email to me, he sends me this: Thought that was interesting? check this one: conjecture 2: there are infinitely many twin Lychrel numbers.

to name some:
2944 and 2946
3583 and 3585
61731 and 61733
79869 and 79871

And also I observed some "freaks" along the way that are in the form L, L+1,L+2, L+3 all being Lychrels!!! for example: 99486, 99487, 99488, 99489. and some in the form L, L+1, L3 and L, L+2, L+3.

Very cool!! Right off the bat, I was inclined to call these "Barone Lychrels". Since he was the first to point them out. Everyone that has written me has been more than generous with giving credit to anyone who makes a discovery, and I think everyone would have agreed with me here too. This seems like a good discovery. It has a definite formula and result. Like (2^n)-1 is called a "Mersenne Prime". However, when I mentioned this to Felipe, he asked me in no uncertain terms to abandon my idea of crediting him like this! In fact he said: PLEASE DON'T DO THIS TO ME!!!!!! LOL! Not at all, thanks a lot, but no... O.K., I won't refer to them as Barone Lychrels, but I think he should get the credit as their discoverer...

I will agree with his definitions though:

Lets use L to denote Lychrel numbers.
Twins: L and L+2 are both Lychrel, they are twins. There are infinitely many twins.
Consecutives: L and L+1 are both Lychrel, they are consecutives. There are infinitely many consecutives.
Sequence: L, L+1, L+2, ..., Ln are Lychrel, they form a sequence of nTh degree. So 99486, 99487, 99488, 99489 would be a sequence of 4th degree.

I can't wait to get a better look at his data or to see what else Felipe comes up with!! My great thanks to Felipe!!

10/4/03 300,000,000 iterations complete!



I've managed to make a functioning 196 app!!!!!

I was waiting for some car repairs today, and with my laptop, I started poking around in LabView, with the specific goal of writing a functioning app. 7 or 8 hours later, I have one running!! It's SLOW AS A DOG!! But I really had no intention of trying to get anything other than a functioning app. I even know of a couple improvements that I could make, that might make it faster, but I have no intention of even trying to implement them... At least, not as of right now... :-)

I expect that it will be far slower than even John Walker's app, but again, that was not my goal. (I expect it will be at least 3 hours for the shallow test!!)

I will get the time of the shallow test on my Comparisons page, when it finishes.

There are a lot of bolds, !!!!!'s, and CAPITALS in this entry, but it's only because I'm so excited at completing something I have tried so many times before, and failed at each time. :-)

Update: It's far worse than I feared!! I have succeed in setting the record for the slowest 196 app ever written!! Yeah for me!! With a time of 4:16:52 I have only completed 1,725 Iterations, @ 716 digits!! Keep in mind, that I didn't purposely do anything to slow it down. I didn't put 30 second delays in or anything... :-) My arrays and digit handling must be miserably inefficient, but I am actually still happy about the whole thing. :-)

9/30/03 Vaughn's application has moved even farther down the timer... He is at 15:44 currently, and at the rate he is going, I expect he will shave at least another 15 seconds shaved off by the end of the week!!

I am still currently using Eric Goldstein's app though. I have said before that I am hesitant to use a command line app, and for right now, Vaughn has not had the time to get his core routine wrapped in a Windows cloak... I'm sure it will come in time.

There were a LOT of notes passing back and forth between Eric Sellers, Eric Goldstein, Vaughn Suite, Matt Stenson and Ben Despres over the weekend. They were all good enough to CC me on their answers. Even though I don't have the slightest idea of the function of the following lines:

pshufw mm0, memory, 27
movq mm1, mm0
psllw mm0, 8
psrlw mm1, 8
por mm0, mm1

I was still nice to read all the traffic. :-) They shared their thoughts on the core algorithms, and the best ways to get even more speed out of all the apps. I thought long about posting the data on a new page, but on one hand, I don't know if all the authors would approve, since they didn't know they would be writing "for the public", and on another hand, it would have been a mess, since there were so many replies to replies, with more replies following those!! I would have spent the next DAY, just trying to format it all out!! If someone really wants to see any of the data, email me, and I'll ask the appropriate people if I can forward their messages...

There was also a bit of traffic, discussing the changing of the benchmarking tests, yet again... Vaughn's point is that the shallow test, is mostly redundant, since memory speed becomes so important for the higher iterations. He is of the opinion that the shallow test ought to be done, using only the number of digits that will fit into the CPU's cache. That might give a clearer picture of the raw core algorithm's performance. Then a deeper one, to test overall app response.

I admit, I was hesitant to test all of the apps over again, but I did. There were indeed performance gains for the apps that suffer from older memory usage schemes. For example, Istvan's app now has a time of 11:31 for the 603,567 iterations tested. But it took over 9 minutes, to get the next 200,000 iterations!! Overall, I'm glad I followed Vaughn's advice. Check out all the updates on the Software Comparisons page.

While your there, you might notice that Matt has improved his app by almost 300%!! Actually, the story from Matt is that Ben improved Matt's app by almost 300%... He writes: Ben deserves all the credit for writing the new non-MMX flip and add assembler routine that I am currently using. All I did was work with Ben to figure out how to interface with it from Fortran. For this new test, his old time was 13:14. He has now cut that down to 4:31. Not as fast as Vaughn or Eric. But I think he's running them down... If so, it'll be the first time that there have ever been 3 people in the heat of the race. I'm hoping he gets down there with them, even though it'll surly mean more frequent testing for me!! :-)

Eric Goldstein has passed 90 million, working with 879.

And finally for tonight... I've added three more countries to the Where Were You page... Bringing the total to 74, they are Jamaica, Kazakhstan, and Mauritius.

9/29/03 I've been in Virginia for a few days, to celebrate my son's birthday with him, and I have a TON of things in my inbox, that I have to sort out... I'll get to it in the next day or so...

Back on the 21st, Matt Stenson was kind enough to compile John Walker's code for me. I wanted it, simply for a comparison test. 0 - 1,000,000 iterations gives a time of 1 hr, 51 min, 45 secs... My thanks to Matt!!

9/25/03 A new deep time of 16:06 puts Vaughn ahead of Eric for the moment on the Comparisons page... With a couple "minor revisions" as Vaughn put it, he has shaved 10 seconds off his app, and is about 3 seconds ahead of Eric. CONGRATULATIONS Vaughn!! This is the first time in a long time that Eric Goldstein has not held the top spot!!

I have been getting regular improvements from Vaughn every couple days for the last few weeks. I am going to be away till Sunday night, (9/28/03) for my son's birthday, but I can't wait to get back, to see new apps in my inbox!!

9/23/03 Check out the Screen shots of all the apps from the Software Comparisons page.

9/20/03 A LOT of changes, to a lot of pages tonight...

I've made another configuration change to my computer. I have added a second 512Mb module of DDR400 (PC3200) RAM to the machine, and gotten some major performance increases from all of the applications tested. It seems that DDR memory is only really effective if you have PAIRS of identical DIMMs. Since I have always used a single DIMM in the past, I never seemed to get the performance out of it. I really suspect that this was the single largest cause of the differences in expected times from Eric's tests and mine. Now my times are right in line with his expectations for the last revision.

I have also changed the CPU from a Pentium IV 2.8GHz with a 533MHz Front Side Bus, to a Pentium IV 2.8GHz with a 800MHz Front Side Bus. That too gave some speed increases from all the apps. (Of course, TODAY, I read about Intel's 64 but chips coming down the line, and the expected price reductions coming also, and I'll have to retest all of these apps again in a few months!!! :-) )

Since Eric Goldstein and Vaughn Suite have both managed to create applications that were so close to each other in performance, it was getting difficult to judge the speed of the apps against each other. I mean how do you determine which app is faster than the other, when they each give 32 seconds for a shallow test, and 3:31 for a deep test?!? As a result, I have changed my comparison tests, to "enhance" any differences between the next generation of applications.

The new times and testing criteria have been updated on the Software Comparisons page. Currently, Eric is ahead of Vaughn, but only by 12 seconds. (This is at 50,000 iterations at 20,000,000 digits!!) It's like the Tour De France... You can race for over 2,000 miles, and STILL have the outcome be decided by only seconds or minutes!! Exciting huh?

Another VERY interesting function of the RAM swap and deeper testing, is that Ben Despres has moved back in front of Eric Sellers for speed, even though his app has not been updated since 6/18/2002!!! I guess Ben's app was REALLY helped out by the DDR ram in the higher iterations!!

Anyway... The new marks, give a better idea of what is going on, so I am glad I spent the entire evening retesting all of the apps. I hope everyone agrees...

I also got thinking this weekend, that if anyone would like to take the time to compile John Walker's original code, and send me an EXE, I would very much like to "benchmark" it!! No improvements, just a functioning EXE. I think it would be a wonderful addition to that page. The original code can be found on John Walker's original Three Years of Computing. page, or on Ben Despres' Lychrel Numbers page.

Vaughn wrote me a email that can be found on the Math Solutions page. It concerns the probability of a given number becoming a palindrome on it's next iteration. It works hand in hand with some of the information Jason Kruppa provided back in October of last year. I've also added some notes I wrote a number of months ago, but never finished... Maybe there is something of interest to someone...

9/15/03 25,000 visitors to www.p196.org!

9/11/03 As it stands RIGHT NOW... Vaughn Suite of Trinidad is probably in the lead with his 196 app. I say probably, since the times are so damn close, and can vary from a single test to the next. In reality, the two apps are so close to each other, that I for one don't feel comfortable calling one ahead of the other. Also understand, that this is changing RAPIDLY! Eric's work recently has made advances, and Vaughn has kept up with him step for step. Added into the mix and confusion, is the fact that I have changed my processor, and BIOS configurations, recently, and there is a lot of things to keep up with!!

In fact, I really need to test ALL the apps again, to get them all onto the same baselines. I'm fighting a really good cold right now, so I probably won't do it this week, but I will sooner or later...

Eric has sent me an update: 2003-09-08 12:26:41 Notification: iteration 205328334, digit 85000000. I thought it might be a good idea to give the credit to Eric and Matt for the status of their searches for palindromes on some of the other Lychrel numbers. As a result, I have started listing their results on the Lychrel Records page. I will update it as they send me info.

9/4/03 I've been testing, retesting, and retesting apps over and over again for the last day. I've actually made very little progress on the actual search in the last week, since all these computer problems lead to system changes, and now app testing.

To help ID the problems with memory, Matt has asked me to test Eric's app with various combinations of the 2.8 and 1.9 chips, with each of the 266 and 400MHz memory. I'm working those tests out...

Meanwhile, Vaughn Suite has sent me his latest app, and has bumped himself into 2nd place on the Comparisons page. His shallow time, matches Eric's right now, at 0:34, and his deep test time is only 7 seconds off the mark at 3:55. (His old times were 0:41 and 6:43) So now, I have ANOTHER page update to make!!!

O Well... I'll make the changes, happily. That's what this is all about after all!! :-)

9/3/03 A few days ago, I fried my 2.4GHz chip somehow or another...

I contacted Intel for warranty work and they had accepted it back for "repair or replacement", but before I shipped it, I was looking over the receipt again, and noticed that I had chosen the "in-store replacement" option that CompUSA (www.compusa.com) offers when I bought the 2.4 chip. (My girlfriend insisted, and now I'm glad she did!!!) It allows you, for 2 years, to bring the part back into the store to get it replaced, instead of sending it back to the manufacturer. It turns out that it's their policy that they will hand you the same part, or apply the PURCHASE price towards an upgrade!! Well, since I bought that chip at around $325.00, they credited me with $325.00. (even though the current price is around $279.)

A P4-2.8GHz in store is $335.11, so I paid the $10 difference, picked up the new warranty (of course!! :-) ) and now have an upgrade to 2.8GHz for $10.00!!!

I also picked up a new ASUS P4P800 motherboard. It supports the PC3200 400MHz RAM, and an 800MHz FSB. Of course, I'm still running the 2.8 at 533, since that's what I have, but now it'll be easier to upgrade in the future.

The long and short of it all, is that my Software Comparisons page is all out of whack right now!! Eric's app now comes in at 0:34 and 3:47!! Of course, there should be a speed increase in ALL the apps on the page, so I need to get them updated.

Matt Stenson, Ben Despres, Eric Goldstein and myself have all been passing a flurry of email over the last week, testing memory speeds, and trying to relate that to why the expected times don't show up sometimes... (In particular on MY machine!!) The theory is that the memory bandwidth just couldn't keep up with the chips about 1.9 and above on the deep iterations. When I upgraded today, I put the 2.8 in the old board (266MHz memory), and tested Eric's app. I got 0:34 and 4:25. This was faster than it was with the 2.4 by quite a bit. But when I put the 2.8 in the new board, with the 400MHz memory, I got times of 0:34 and 3:47!! This seems to validate Matt's, Eric's and Ben's ideas that it's a memory speed problem.

Now, with any luck, I should be able to come very close to expected times, as Eric continues to make improvements...

Actually, at this point, I think it might be time to change my benchmarks... and bring them up a bit, to get them back into the 2 and 10 minute range, that these apps started at... I'll get them all updated soon!!

Update: The Software Comparisons page is now accurate.

8/31/03 After a few days of having my machines all off line for one reason or another, I think everything is back up...

Eric Goldstein sent me another speed increase for his app!! As you'll see on the Software Comparisons page, he is now down to 41 seconds for the shallow test and 5:01 for the deep iteration test! So now he has the fastest app for both of the benchmarks, where before Vaughn Suite and Chris Lomont had the edge in the shallow, and Eric had the fastest in the deep iterations.

What is bothering Eric's mind as well as my own, is that he tested and got a 20% speed increase for both benchmarks, where I got a 20% increase for the shallow, but only a 7% increase in the deep. He was fully expecting a deep time from me of around 4:30. I REALLY wish I knew why there was such a discrepancy between his testing and mine!!! (I'd sure like to have that extra 30 seconds per 20,000 iterations, over the long run!!) :-)

I'm sure, Eric's genius will eventually figure out why my machine is so much slower than his...

8/25/03 Eric Goldstein has shaved a few seconds off his times! While reviewing his code for the first time in a while, he noticed a new twist, and while it did not make a drastic improvement, he pulled 2 seconds off his shallow time, and 8 from the deeper test... That just makes it harder for everyone else!! :-) Great job Eric!!!

Matt Stenson has also managed to cut a bit from his app. Currently Matt's app is pretty far down this list, but he is using it for his own purposes, and not really for mine, so he appears content with it's speed. However, he may decide to jump in the speed fray yet... He currently has the Lychrel number: 1997 a bit over 13,000,000 digits.

Don't get the feeling that I think Matt's app is bad!!! Remember... I never could get one working, so I really admire those of you who do!!! He has incorporated a "MOD-9 checker", a log file, and nice timer, all in a very user friendly, simple interface. My thanks to Matt for letting me "play with it"!!

8/24/03 About the only issue of note, is the addition of Peru to the Where Were You page.

And of course the completion of 113 and 114 Million. :-)

8/12/03 I'm sure that I won't be making an update in the next couple days, since I seem to have gotten so lazy... So I'll make the comment now, that in three more days, (8/15/03) I will have been running the 196 quest CONTINUOUSLY for 2 years. Of course, I was running it a bit before that, but with such a large gap in between the dates, I don't count those.

Eric Goldstein has crossed 80 Million digits: 2003-08-08 02:02:20 Notification: iteration 193249387, digit 80000000.

I seem to have misread the email quoted below from Matt Stenson of Australia. He had written me, and explained that he ran the 196 search to 10 million before he found my pages. After reading where things stand, he has moved over to the numbers 1997, 10553, 10563 and 36,973. As of the email dated 7/24 1997 is in the lead at around 8 million digits. Matt, I apologize...

My thanks to Steven Van Hulle of Belgium, who was kind enough to let me know that the tables on the Identifying Lychrels and the Lychrel Records pages were not rendering correctly in Mozilla. I didn't see them, since I use Opera and occasionally IE6, but I think I have them corrected now... If they're still whacked out, let me know, and I'll try again!!

That about takes care of it for today...

7/26/03 As I said last month, I still have my son for the summer, and I have been doing so many things in general, that I just haven't taken the time to sit and get this site updated. There are a number of mentions I want to make though, mostly from everyone else, so here I go...

Back on 7/2/03, Jason Doucette emailed me with the following news: A new record was solved today. The 17 digit number 10078083499399210 solves in 233 iterations.

Then on 7/10/03, he emailed me again, to say that A new record that beats the old record: 17 digit number 10442000392399960 in 236 iterations

Remember, you can get to Jason's work at http://www.jasondoucette.com/worldrecords.html

On 7/6/03, Eric Goldstein sent the following update on his 879 quest: 2003-07-06 03:17:34 Notification: iteration 181171499, digit 75000000 I believe that he's actually "catching" me, as far as digits vs time. It's good for me that he's not working on 196!!

Ben Despres and I have both heard from a gentleman in Australia named Matthew Stenson. I seems Matthew read about the 196 quest back when it was mentioned on Slashdot (See Archive for 8/18/02). He then downloaded John Walker's code and 1 million digit number to play around with. After some changes, modifications and general poking around, he has been running it ever since... He currently is a bit over 10,000,000. Congratulations Matthew!! And it is great to meet you!

I've added three new countries to the Where Were You page. They were Costa Rica, Paraguay, and Saudi Arabia. :-)

I have spent very little time trying to work out the repetition question discussed earlier, but I'm sure I'll get back to it in another month or so, when the summer is over, and the kids go back to school.

I hope everyone across the globe is doing well...

6/27/03 I have my son for the summer, so it's been kind of "slow" in the 196 world, but I have been trying to track down the repetitive vales discussed earlier in the month. I'm convinced, that there is nothing of interest to anyone, So I'm not putting up my notes yet...

6/17/03 I have gotten some good feedback on the paper from a couple people. I'll look at them all more in depth in the weeks ahead.

One of the "discoveries" I made today is the first digit repeating pattern cited by Kevin Brown in the paper here, is coincidently very close to the one I mention in my paper.

From the digit string 17509097067 Kevin found:

175 09097 067
935 88187 638
177 266376 177
948 940038 948
179 8770088 797
977 7570867 768
184 55251625 547
930 07866881 028

In the 196 iterations I found:

184 768
930 547
175 028
935 067
177 638
948 177
179 948
977 797

The pattern of the first three digits are the same!!!!!!

I checked, and the string 17509097067 is not one of the iterations of 196.

This strikes me as an amazing coincidence!! I'll look into it more tomorrow.

6/10/03 I've made an update to the end of the paper described below. If you have already read the paper, you might want to scan it again for the changes at the end of the document. If you have not already read the paper, both links, now point to the updated version, and you can ignore this message. :-)

The paper is HERE.

6/8/2003 19:35 100 MILLION DIGITS!!!

6/7/03 I seem to have a lot to mention today!!

We are FAST approaching the 100,000,000 digit mark!! I expect it around 21:08, on 6/8/03.

There are 5 iterations that produce a 99 million digit number. The first is: 239,175,318. Eric Goldstein has commented that this is the most that can be generated before a new digit is added. The 1st and last digit orders would have to be 1,0 / 1,1 / 2,2 / 4,4 / 8,8. The next iteration will force a new digit being added.

By the way, Eric sends the following: 2003-06-04 15:11:47 Notification: iteration 169093790, digit 70000000

Vaughn Suite's application is getting better and better, but is still off of the mark that Eric has for higher iteration testing. The last test I ran, had it running about 1/2 speed in the deep iteration testing, even though it is faster in the shallow tests. Vaughn is working on it...

I would appreciate any comments on the following:

Adding to the work begun by Ben Despres of the USA, for file verification, I was playing with verifying correct iterations by dividing by 9. Ben's work dealt with the checksum value of an iteration, to derive the formula:

Cx = (C0*(2^(x MOD 6))) MOD 9

And is more fully explained on the File Verification page.

What I found was that it can also be shown that a similar but simpler equation can be written for the value of the iteration itself. The formula:


can be used to verify the iteration's validity. In this newer, second formula, A is the current iteration's digit string, B is the digit string of the next iteration after A and INT is an integer. If INT is not an integer, then an error has been made during the iteration. It follows that the same test can be performed dividing by 3, since 3 is a factor of 9.

I am VERY unsure if this is of value or not. Lacking programming experience, I did some research on Checksums. But I can't say that I ever TOTALLY understood what was going on! :-( My uncertainty, in particular, concerns if this is actually the same result produced by Ben Despres' formula, or if it is in fact a simpler method of checking the validity of an iteration.

Of interesting note, the majority of results from the division will be palindromes. Unfortunately, this does not hold true for every iteration.

The first 29 iterations for 196 show the results nicely. Using the formula "(b-(a+a))/9=" gives the following results:

55 . 00

-11 . 00

454 . 00

-121 . 00

2772 . 00

-1221 . 00

-110 . 00

77077 . 00

957748 . 00

-366641 . 00

-122210 . 00

-1100011 . 00

-1100011 . 00

488400 . 00

-122100 . 00

-1222210 . 00

-11000 . 00

593101375 . 00

-121000121 . 00

418221824 . 00

-1100000011 . 00

20981818902 . 00

-122222210 . 00

-11001221 . 00

577888888786 . 00

-12210000 . 00

5502163612055 . 00

-1100012210011 . 00

48447977974484 . 00























Or am I all fouled up?!?!?!?

And finally, I have a paper that I would like opinions on!! It is concerning the theory that Lychrel numbers develop into an infinite repeating pattern of digits, like the one we have seen for numbers in other bases. I figured that one of the methods for figuring this out, was to simply start looking for repeating strings across thousands of iterations. (Currently, my test data is covering 127,985 iterations!! That's a bit more that 122 GIGABYTES on my hard drive. :-) )

Anyway, my limited knowledge of statistical functions has kind of brought me to a halt, before I could make any proofs. I have continued poking around this line, but if I find an answer right now, it will be as a result of an accident, instead of any well planned direction. I would REALLY APPRECIATE it, if all of you could look over this paper, and give me any feedback. I am not even sure if there is ANY merit to what I have spent the last month working on, but it's time for someone else to look at it, and tell me that I'm wasting my time, or that this is something that I should pursue a bit more. (And if it's something to pursue, any advice would be welcome!!)

In addition, if any of my "assumptions" are wrong, or my methods seem to be wrong, please let me know. There are many times I feel I am solidly on the right track, and many times I feel I'm spinning my wheels for nothing.

The paper is HERE. in a MS Word document. If anyone would prefer it in straight text, let me know, and I'll get it to you. (Without the charts though...) THANKS IN ADVANCE!! to any opinions.

5/26/03 Vaughn Suite has improved his application's speed again... He is currently at 50 seconds for the shallow test. This beats Eric Goldstein's tine of 54 seconds. But, just as Chris Lomont's app was faster for the shallow test, it may turn out that Vaughn's will be slower in a deeper test. I am waiting for him to complete the load functions of his app, so I can do a deeper iteration test. I'm really excited!!

Vaughn also mentioned in a couple of his emails to me, that he is in contact with some one with the "alias" bitRAKE, whom has also created a 196 app. Vaughn says that bitRAKE's app, should actually be even faster than his own...

Eric G is heading back to the keyboard, to try to pick up some new ideas. It should be an interesting month of development!!

Jason Doucette was kind enough to give some updates on the earlier dates for some of the milestones. He in fact found out that someone had beat him to 10 Million. I've made the updates as I understand them right now, to the Milestones page. It is possible that I misunderstand the email, so if the table doesn't look right to anyone, please let me know!! I will also get Mike's last name up as Jason lets me know what it is.

5/17/03 Eric Goldstein is at 65 million digits in his search of 879. 2003-05-14 00:58:24 Notification: iteration 157014340, digit 65000000

I heard from Dr. Vaughn Suite of Trinidad a number of months ago, probably in December or January. He gave details of his p196 coding experience to that time (unreal mode DOS program), and problems with slowing down on Pentium 4's, and promised a working program by the end of the month (January). Back on 5/13, he finally delivered! I'm testing now...

It is still a "work in progress". It will not load any of my files, and is forced to stop at 1,000,000 digits, but he wanted to see if he was on the right path.

Turns out he's on a pretty darn good path!! His 0 - 413,280 Iterations time is 1:05!! Which puts him #3 on the all time speed list. for the shallow test. Congratulations Vaughn!!!

He said in the note that accompanied his app, that he has run smack into the same Windows XP problem that Eric G. had, in that large files are horribly slow. He believes he understands why, (As Eric must have figured out, obviously!) and will get a new version to me as he has time. For now, I have put all I know on the Software Comparisons page. There's not much there, really, but he does deserve a place on the list.

Again my congratulations to Dr. Suite!!! I wait to hear from him again!!

5/10/03 I got a note from Eric G. back on 4/24/03: 2003-04-24 11:22:17 Notification: iteration 144,934,204, digit 60,000,000

Remember... He is running the thread for 879...

4/17/03 I've apologized enough for my sluggish updates. Everyone will just have to get them as I "get around to it". This one is actually quite recently compared to any "news". There hasn't been anything major other than milestones.

I have gotten an email today, from Jason Doucette, saying he completed his Longest Delayed Palindrome search through 16 digits! Remember, his "World Records" site is here. The email and "stats" that he sent me can be read on my Other People's Notes page. So far, there is not a single number that solves in greater than 201 iterations, and NOTHING solves in exactly 160 iterations.

As a small update, I got an email from Willy Roa on 4/10/03. He is the author of This Page That I mentioned on 7/6/02. He tells me that he is a science writer, and from what I gather, he and a group of people write technically oriented clips in Basque. He says Basque is a minority language, and that there are fairly few palindromic sentences in the language. I learned something new. :-)

I am letting the Lychrel app run, on the 15 digit numbers for now, but I'm kind of discouraged... It says that it will take 354,521,853 more years to finish. Ben is looking into a "possible" problem. :-)

One thing I've noticed, is that I haven't gained a new country on my Where Were You list in quite a while. (probably 6 months.) I'm still getting between 20 and 40 visitors a day, but no new countries. I guess there are only so many countries in the world, that have enough people who have access to the web, that statistics catches up to me. I just thought it was odd...

Oh yeah... I also finished the 86 - 89 milestones. :-) I'm getting excited to hit the 100 million mark.

4/2/03 Let me be frank...

I've had fairly good weather for the last few weeks, and when that is combined with my telescope, I haven't been sitting in the house working on the computer!! In fact, I've been hauling computers outside, so I could try getting some CCD images from the telescope. I've been building different mounts and things for getting a CCD attached to the telescope. It has been frustrating!! Most of the images are fairly poor, but some of them have been very nice. Anyway, that is probably single biggest reason I have not been updating these pages...

HOWEVER!!! I'm sure that everyone believes I am still counting higher!! And of course, I am... I passed 83, 84, and 85 since I last wrote.

Also, on 3/31/03, after 76 run days, the computer finished the 14 digit Lychrel list. It added 4,455,557 numbers to the list now totaling 9,693,937 identified Lychrel numbers! Ben's app allocates memory for X number of Lychrel numbers when it starts, based on available system memory. I have 640 meg of RAM in that machine, so Ben's app will run until just over 19 million Lychrels are found. (I don't remember the exact number, that it displays it on startup.) Looking at the way the numbers progress, on the Lychrel Records page, I would suspect that I will not be able to finish the 15 digit numbers, before it runs out of memory. Depending on how it looks in a month or two, I may just break down and add more to the machine, to finish the set, but that's a long way off still!!!

Everything else is moving along nicely. Ben says he is ready for the Maine winter to be over... :-) I'm sure Eric G. is busy, busy, busy, with his new son. And as far as I know... the rest of the world is just idling along smoothly.

I don't promise to make more frequent updates, but I do promise that I am still processing!!!

3/21/03 I have crossed 200 million iterations!! It was sometime around 11 a.m. this morning. For some reason, the app didn't save the iteration, but it's no big deal. I have one from about 3,500 iterations earlier, so I could recreate it if I want to. Maybe another day...

There are 5 iterations that create an 82 million digit number. This is the only milestone that I can remember that has had so many iterations. The first one was 198,109,015

Eric Goldstein has sent me an update for his 879 search... 2003-03-20 17:59:40 Notification: iteration 120,779,988, digit 50,000,000

Ben Despres was kind enough to send me an icon for the headers of these pages. My thanks to Ben. It's small, and unimportant, in any true sense of things, but it was VERY nice of him to do that for me!! You SHOULD see it on the title bar of your browser. (If I installed it correctly!!)

S├ębastien Veigneau was good enough to send me the source code for the 196 app that he and Vincent Prosper used for their work. It can be seen on Ben's Website

The real tracker stats tell me that I've crossed 20,000 visitors!! Considering the Slashdot article back on 8/18/02 generated around 8,500 visitors in two days, I'm more than happy with the other 12,000 visitors. They've come from all over the world, as can be seen on the Where Were You page. Welcome to all of them!!

3/16/03 I've added a link to Jack Driscoll's page on the Software Comparisons page.

3/8/03 I hope no one is waiting for updates to happen to this site, for anything time critical!! 1/2 of the problem is that Eric's application is still turning out a new milestone, in around three says, and I just don't get around to updating this site that frequently. Another part of it, is I have been in my workshop a lot lately, and not sitting in front of the computer. The third part of it is that I have bought a new telescope, and have been standing outside in dark, looking at the cosmos. It all boils down, to the fact, that sitting here, updating the web page, has kind of taken a back seat. Sorry...

Today, I get the great news, that Eric Goldstein has become a father!! Dennis Goldstein was born on Thursday, March 6th, 2003 at 07:30 AM (I assumed this is Netherlands time. :-) ) He was born quite big at 54cm and 4.430 kilograms (21.25 inches and 9.7lbs, for us Americans...). Everything went fine for mother and child, who are both healthy.

I'm sure everyone agrees with me when I say Congratulations!! to Eric and his wife Kitty!!! I wish Dennis the best of luck in this world!!

2/25/03 I've been goofing off with so much other stuff lately, that I have found it very difficult to keep this site up to date...

I don't have any news other than Eric Goldstein's progress on 879: 2003-02-24 02:01:02 Notification: iteration 100,000,000, digit 41,398,614

If nothing else, it's nice to see that 879 also has that 2.415 iteration to digit ratio. :-)

2/20/03 It's been a while since I updated this site. :-( I've just been lazy... But that doesn't mean I haven't been running. In fact, I've added 74 and 75 million to the Milestones page since my last blackboard entry...

Eric Goldstein was kind enough to send a new version of his app, which now includes the ability to save the file with no formatting. Not needed most of the time, but when I was trying to load some of the numbers in LabView, I was having problems with the line breaks and offsets and things like that. In an effort to simply make it easier for me, he added this feature. The other new update, is that he has now added a Mod-9 test to his app. It will test the number on startup, and also at each save point. This should help me avoid the problems I was having before, with running a bad number. From now on, if the number isn't good, it just flat out won't process it. I really hope all future apps from ANYONE, includes this function!!

On the Mistakes and False Starts page, there is reference to a post by Vinny Romano, that I had serious doubts about... Well, Vinny was good enough to write me, and set some of the facts straight!!

With respect to http://home.cfl.rr.com/p196/false_starts.html, I agree that my claim of having gone to 24 million digits was not correct...I would say I probably simply forgot a decimal point and actually only achieved 2.4 million...or maybe it was only 1 million digits and 2.4 million reversals...I don't know... If I recall, the program I wrote was much more efficient than the one that was used by John Walker, Tim Irvin and Larry Simkins for their 2 million achievement. Furthermore, I too was running my program on a 'supercomputer' at the University of Maryland, not a P90.

I've been away from this problem for years now...I just happened to be surfing and I came across your page...


I was really happy to hear from Vinny!! In my OPINION, if he had simply been boasting in the post from 1995, and didn't do the work, he surely wouldn't have written to me now, to correct it. He would have ignored it altogether, and we would have never known. The very fact that he was reading this site, tells me that he was at least still thinking about the 196 search, and was looking around the net.

Vinny, THANKS for setting the record straight!!! I'm sure you deserve some credit for your work, so if you can firm up some of the data or dates, or anything, I'll try to get you into the correct "chronological history"...

I crossed 75,000,000 digits yesterday, 2/19/03...

2/10/03 175,000,000 iterations produces a 72,433,237 digit number!!

Eric Goldstein commented that the 9's in yesterday's post, actually could be considered 1's instead. From his note:

I think that the 9's should be 1's too. e.g. 9 minus 0 equals 9, but 9 plus 1 equals 0. So the difference between 9 and 0 is actually 1. See what I mean?

More generally speaking: if the absolute difference (a) is greater than 5, then a = 10 - a. This will result in differences that are always less than or equal to 5

I have to say I agree with this thought. As a result of this idea, I rearranged the Boolean tests I was doing in LabView, and re-calculated the file from yesterday. Now, the 100,000 digits of iteration 2,417,447, ONLY contains 0's and 1's. I'm going to redo the other files I have, and see how some of the other iterations behave...

2/9/03 Everything has been going smoothly the last few days. That's good!! :-)

I got another notification from Eric Goldstein: 2003-02-08 16:57:23 Notification: iteration 84542533, digit 35000000. It's good to have one of the other numbers being followed out. I keep hoping to get an email from him, saying that his XX million iteration matches one of the ones on my File Verification page!! :-) It would sure stir up some of my thoughts about 196 being "magical" all over again, if the 2nd Lychrel number joined up with the same thread!!

I was following up a bit with the thought that I had on 1/23/03, about some of the iterations, being a palindrome for quite a few digits, then breaking apart... Eric Goldstein mentioned, that it was interesting to notice that in a good many of the iterations, the absolute difference between digits was often 1 or even 0. Obviously, if all the differences were a 0, the number would be a palindrome. Iteration 2,417,447 actually goes 15 digits, before it breaks down. I know 15 digits out of a million is pretty weak, but it was still interesting to see.

The file here shows the first and last 20 digits of the iterations between 2,415,837 and 2,420,837, along with the absolute difference between the digits.

Most of the iterations that have a lot of 1's and 0's, actually have more of 1's and 0's than any other number. They seem to be very close to forming a palindrome. For example, 100 places of iteration 2,415,884 looks like this:


Carried out even further, the same general clusters of 1's/0's and rare odd numbers follows...

In fact, if you look at 100,000 digits of iteration 2,417,447, there are ONLY 0's, 1's and 9's. In some other cases, there are other numbers like a 6 here and an 8 there, but they are "rare".

Then I manually reformatted the file, (the 2417447 file) and ran it through Ben's file checker program. Of course it failed all of the checks, but I was curious if there was a visual pattern in the 1's, 0's and 9's... As far as I can tell, there is not. I looked at it in dozens of different pixel modes, including the programs "auto-mode". Nothing but the typical "static pattern". Although it does look a bit different from what I'm used to seeing, since there are only 3 pixel colors!!! :-)

Is this useful?? Is it in anyway helpful?? I don't know... Neither did Eric or even Ben. I throw it out here, so that someone with other ideas, can think about it, and maybe give me an idea of how it might help solve any of the million questions that make up this site.

2/6/03 I have had a hell of a time keeping things straight this week!!! I've had a few errors happen this week, and they have all been my fault! :-( But I feel like I'm over the "shock" of the Columbia explosion, and decided today would be a good day to get this site back into shape.

I finished the 71 million data set early yesterday morning, but I had mistyped the save directory in Eric's ini file, and it didn't capture it. I'm running it again from 70,996,903, which happens to be the save point just before the "error". In fact, by the time I have this page updated, it will probably have finished, and there is no reason to even post this, but...

I never did exactly figure out what was going wrong last week... I have simply been checking the files a couple times a day. I haven't come up with another "bad" file yet, but I was really starting to think there was something wrong with Eric's app!! For some reason, I didn't think it wanted to get that 70 file complete! Turns out, that everything seems to be fine, Eric's app it rolling along smoothly, and if I would put in the correct data into the ini file, all would be well! :-)

I was smart enough to save the file from this afternoon, before I re-ran the 71 section. That way, in about 20 minutes, when 71 is complete and safe, I can go right back to 71,389,992 from above... :-)

Eric Goldstein forwarded a line from his log for 879: 2003-01-29 02:18:01 Notification: iteration 72466349, digit 30000000

2/1/03 It's been a very long day for those of us who live right here, (within 15 miles) near the Kennedy Space Center... Most of you know that until Feb of 2002, I was working at KSC... I have a lot of friends at the Center, and I am thinking of all of them. I am an AVID space supporter. I watch the launches to see the most complex machine ever made by man, and marvel at the miracle of it's success. I saw Challenger explode in 1986. Now, there is Columbia... I have watched EVERY Space Shuttle launch since the first launch of Columbia in 1981, if I was living in Florida. (I actually missed a few while I was in the navy, but not that many.) Since I worked at KSC, probably 1/4 of the launches I've ever seen, I was at the 3 mile limit for access. (Where the VIP's get to sit. :-) ) This was the first launch that I was ever in the area for, that I missed!! I didn't even know about it on launch day...

I have seen most of the landings. I had no intention of going anywhere to watch this one, but I would have been able to see it from my back yard. It's a sad day...

This was about two years ago...

I finally got a valid 70,000,000 file. I have done the 70 data set 4 times!!! The one, posted below as an error... Then as I was working it again, I ended up with two DIFFERENT invalid files... I don't know what in the world is going on!! I am watching the files VERY closely as of late. Currently, it is O.K., I keep expecting to find another problem...

With all the activity today, I don't feel like posting the milestone and data... I'll it all up in a day or two...

1/26/03 Yesterday morning, the 13 digit Lychrel numbers finished. There were 4,451,740 new numbers added to the list, bringing the total to 5,238,380. I don't think I'm going to do the 14's right now. Maybe in a few days or a week, but for right now, I want to use that machine to play with some of the datasets.

1/23/03 I have to admit... right at the moment, I don't have the slightest idea of how Ben made the following image, but it sure looks nice!! :-)

His comments that came with the image are this:

I've started looking at the fractal nature of reversal-and-addition, which I briefly mentioned once before, but have started looking into seriously. I've made one good preliminary image of the attractor, which I've attached. It represents the mapping of the palindromeness, in the 4d Kins-space (the 1e8 range in base-10), unwrapped into 2d. I've tried different 2d mappings to get better clustering of palindrome-reaching points, but it has proven exceptionally difficult.

You will probably notice that each section appears to neatly subdivide into two areas, recursively... This has so far proven an illusion, and attempts to clarify the image based on that binary nature give something that looks very much the same, amazingly enough.

You may also notice (if you've seen these structures) that the parts of the image bear a strong resemblance to the Sierpinsky carpet and triangle. This doesn't really surprise me, but it does give me hope that a proof may yet exist for whether or not Lychrels really exist.


Maybe someone will see something interesting in there... I leave that for others right now.

As an example of a totally free afternoon, I was reading all of the papers on the new Math Solutions page, for about the 100th time. (I'm trying to really understand what is going on on this site!! :-) ) Anyway, the paper: Self-Similar Reverse-Sum Sequences written by Kevin Brown, got me thinking about my own files, and whether they have this recurring pattern anywhere.

I didn't find a recurring pattern in the 175 iterations, from 1,000,000 to 1,000,065, (well, I did, but it was all in my imagination, or stretching the fact so far, that no one else would have agreed!! :-) ) but I did find a few lines, that I hadn't expected to see!! There are quite a few iterations which begin to form palindromes, but fail after 5 or 6 digits. One of the example lines, (Iteration 2,415,848) actually makes it to 10 digits, before the palindrome breaks down...

I had a lot of free time this afternoon!! I doubt that this is any significant finding... But it was fun. I was surprised, maybe someone else will be. The result file is here if you want to take a look.

1/22/03 It appears there is good news for the future of the word "Lychrel"...

Some clarification that I got from Vincent Prosper is that "Kin Numbers" are only the ones that relate to each other, and do not form a palindrome, not the class of numbers overall. It actually works out very well for my purposes!! I had made the following comment on the Lychrel Records page:

I've had people tell me that numbers like 295 and 394 should be called Lychrel numbers. I have never agreed, and am happy that Ben's application does not include them. If anyone else wants to name the "extra" numbers, I'll be happy to try to use the name. Otherwise, maybe I'll come up with something...

Now, it turns out, that someone already HAD named the "extra" numbers. So I am going to update that page... And from now on, I will make it a point to try and differentiate between Kin Numbers and Lychrel Numbers. :-)

Of course, I'm still listening to arguments from anyone who wants to offer a different opinion!!

Vincent was also kind enough to send me a copy of his 2001, joint paper with Sebastien Veigneau, in PDF format. You can look at it on the Math Solutions page.

Ben's Lychrel app has an expected 6 days left to complete the 13 digit numbers. There are a little over 4.9 million Lychrel numbers currently in the 240 megabyte list.

1/21/03 O.K... I think what happened, was that at some time, as I was backing up an ACTIVE file from between 67 and 68 million, and it got messed up. The newest 68 million file did not match the one that I had, that had been reported as bad by Ben Depsres' checker application. Luckily, the new one does pass Ben's app!! :-)

So.. I've lost about 2 weeks of progress... No big deal... Again, it could have been worse. It could have been 2 months!! Eric Goldstein's app is so fast, that I expect to have it all recovered in about 9 days.

I guess I need to get back into the habit of checking EVERY milestone, instead of just random ones!!

1/19/03 I got an email from Vincent Prosper of France today, in which he had a lot of things for me to think about, change, and update.

One of the items he talked about was this:

In the process of computing numbers that can't lead to a palindrome, a lot of operations are irrelevant. When you compute 196+691, you also compute 295+592, 394+493, and more generally 2 x [ (7/2)9(7/2) ], where 7/2 should be considered as a (pseudo-)digit. That is to say, 196, 295, 394, ... all belong to the 'class' of the pseudo-palindrome 7/2 9 7/2 (where 7=1+6, 2+5, 3+4). We characterized these 'kins numbers' without any trouble in our article for any basis. I saw on your web pages that you call them 'Lychrel numbers' for the decimal basis. Please update your ethymology/history: they were called 'kins numbers' by a Japanese mathematician K. Yamashita (see http://www.jams.or.jp/mj/45-1.html for references) in 1997, and we, together with S├ębastien Veigneau, gave the right math definitions in 1998 - published in 2001.

I asked him for a bit of clarification. If in fact Koji Yamashita (or Vincent and Sebastien) described "Kin Numbers" as including 295, 394, 887 etc, then I am reinforcing the idea that a Lychrel number is only the ROOT number such as 196, 879 or 1997!! On the other hand, if they called 196 and 879 "Kin Numbers" but not 295 and 887, then I have to admit that I am VERY disappointed, by the loss of the name Lychrel Numbers!!!! So I until I'm corrected... Kin Numbers are the list numbers overall, and Lychrel Numbers are the root numbers of any thread, like I've always claimed.

He also pointed out that:

The result given by Jason Kruppa - 10 Oct 2002 - in your web page Blackboard Archive, was also mentioned in our article (last page, Appendix B 'Lucky numbers')

Their article can be found Here. I had read their paper, but since it had been so long ago, I did not recognize Jason's comments as a duplicate of Vincent and Sebastien's work. I still thank Jason Kruppa for his contribution, but I think the "discovery work credit" should go to Vincent and Sebastien.

Also, the PROBABILITY page has been removed altogether, and replaced with one titled Math Solutions. it is an attempt to gather information for a "logical" conclusion to this quest, instead of the "brute force" method I am currently using. Maybe there is something of interest to you math oriented people.

On another note, my girlfriend found a story which made us both smile. Luigi Morelli had let me know in the past that it was in the works. It's nice to see it on the web. I assume that it is only meant to be a very short story. The original Italian version is at: http://online.infomedia.it/riviste/dev/103/articolo04/articolo.htm. For those of us, who don't speak Italian, a rough translation can be gotten from Google, here. It's coherent enough to make me smile. If anyone can provide a cleaner translation, I'd love to have a copy. I emailed Luigi to tell him that I'd seen it. Maybe he'll provide a translation... It was nice. And from now on, I am going to have my girlfriend start calling me a "lofty mind of the planet"!!! :-)

1/17/03 Something has gone wrong... The data files since 67 million all fail to pass Ben's app...

I've tried quite a few different things to identify whether the problem is in my files, Ben's app, or Eric's app. So far, everything points to a corrupt file.

For right now, I'm running 67 to 68 again, and going to look at the results. I am leaving all the milestone info on the site for right now, but I have to assume that everything after 67 will turn out to be wrong, and will be replaced.

Wish me luck...

1/14/03 A few random updates tonight...

I have found a drawback to using Eric Goldstein's application. The problem is that since it is running so fast, it is completing milestones, faster than I can (o sometimes even feel like) update the pages, and keep this site current. :-) (That's a joke. :-))

Seriously, his app is turning out a new million digits in about 80 hours. It's great.

I am beginning to think I need to reformat some of the pages now though... Having all the dataset information, for example, on the same page seems to be getting cumbersome. Maybe it's just me, I don't know.

As noted below, Eric Goldstein has stopped following me on the 196 quest. He is currently running the 879 thread. He sent me the following line from his log file:

2003-01-13 09:56:51 Notification: iteration 48,304,915, digits 20,000,000

As he keeps me posted, I'll post them here. It would be really great for 1 of the two searches to find a palindrome. It would create a really huge question mark on this entire project!!

As far as the Lychrel search... Currently Ben Despres' app is working on the 13 digit numbers. It is finding an average of 2.9 new numbers every second. As of 1:10am GMT, 1/15/03, there are 3,516,077 Lychrel numbers in my list. The program expects to finish the 13 digit set in another 1,278,456 seconds. (Almost 15 days.) The thought of 1.3 million seconds is kind of funny. That's the way Ben's app displays expected time remaining. I like looking at it that way. :-)

I guess that's it... More as it happens...

1/7/03 Ben Despres has sent me a copy of his Lychrel Search program. It is now running on my 1.9 GHz machine. He has made some pretty impressive advances in search speed. If I remember correctly, during the summer, it took him around four days to calculate all the numbers from 0 to 8 digits. Today, I managed to do 0 to 11 digits in just over 2 1/2 hours!! Very Cool!!

I have made some massive updates to the Lychrel Records page.

My intent is to let that app run full time on the 1.9 GHz machine. Ben estimates that my 640 Meg of RAM and 40 G-byte hard drive, should last till about the middle of 1e14. (~19,153,856 discovered Lychrel numbers.) Then I'll have to upgrade, or someone will have to figure out a better way to search. :-)

1/4/03 I got the following note from Eric Goldstein:

Well, I stopped my 196 search (quite a decision, actually) and started 879 at Jan 3rd 2003, 11:40 pm GMT +01:00 from iteration 24153360.

Now I can only hope to find a palindrome before you do!


His thoughts being that since he had finally gotten his app to run as fast under Win XP as on WinME, and since he and I were both using the same app now, and finally that my machine was faster than his, that he would run on number, instead of "running a losing race". I imagine that, that was a hard decision for him to make. I have thought a few times, whether I should continue or not... I've always said yes. :-) I sent him my existing 10 million digit number to give him a head start, and he's on his way...

1/01/03 I hope that everyone had a safe and happy New Years!!

I am not a very religious person. Very little in fact. But I got an interesting email yesterday from Dennis Nelson in the USA. He writes as follows:

Genesis 1:1 in Hebrew has 7 words and 28 letters with the Hebrew sum of 2701. Now 7x28 = 196. To me this number is easy to understand.

Maybe he's on to something...