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196 AND OTHER LYCHREL NUMBERS

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In my mind, there are certain people who deserve recognition for work in the quest to solve 196 into a palindrome. From my countless hours of looking and thinking about this challenge, there are a few names that jump out and say "RECOGNIZE ME!!"

I list them here, and why I think they're important. I tried to be very accurate with my dates and times, but it is a bit difficult trying to keep data from 4 or 5 web sites straight in my head. Please let me know immediately, if you think I've made an error in quoted times or dates. If you disagree, with someone I've left off, or why I've included someone, I'd love to hear from you. We can discuss the issue, and maybe, you'll change my mind.

I could not have proceeded in this quest without the help of most of the people below. They all are amazingly friendly and have put up with my ignorance and questions. I really do thank them all!!!

In no particular order other than time, here is my list of people who should be recognized in the quest for a palindromic solution of 196.

C.W. TRIGG: So far, I know of two references that mention C. W. Trigg. Both were found by Jason Doucette from a Math Central page:

The first is: C.W. Trigg, Palindromes in addition, Mathematics Magazine , 40 (1967) 26-28.
The second is: Heiko Harborth, On Palindromes, Mathematics Magazine , (1973) 96-99

According to the post on the Math Central page, the 1973 paper states that "Trigg checked all integers less than 10,000 in 1967 and found that 249 seemed to never form a palindrome. 196 would be the first of those 249 numbers."

PAUL LEYLAND: Sometime around 1972, 196 had been carried through 50,000 reversals and additions by Paul C. Leyland yielding a number of more than 26,000 digits without producing a palindrome. Paul explains his program in an email from August 19, 2002 which can be read on the Other People's Notes page:

"The work you refer to was done about 20 years ago on a 4 MHz Z80-based machine running CP/M. The core reverse&add and the palindromicity detector were written in assembler and the I/O etc was written in Algol-60. The machine only had 32K of memory (actually rather a lot for those days) and I ran the program until it ran out of memory --- which explains the limit chosen for the number of iterations." - Paul C. Leyland

F. GRUENBERGER: This is another reference found by Jason Doucette. In the April 1984 Scientific American "Computer Recreations" column, an article appeared about mathematical patterns (F. Gruenberger, Computer Recreations, "How to Handle Numbers with Thousands of Digits, and Why One Might Want To.", Scientific American, 250 [No. 4, April, 1984], 19-26.). Although I don't think either of us have actually seen the article yet, I have to trust that the information given here is accurate.

P. ANDERTON: Jason Doucette's website says: Again, P. Anderton (in 1987, according to this Google Groups continued the process up to 70,928 digits (170,000+ iterations) without encountering a palindrome. but I didn't see this particular reference. I have asked him for clarification, and will update this entry as he gets back to me.

JOHN WALKER: Universally, I think everyone would agree that John was the pioneer of what has become known as "The Quest". Of all the pages I found that had some... let's say "serious" discussion of 196, Mr. Walker's site is quoted by them all. His 1987-1990 three year commitment to solving 196, really started it all.

TIM IRVIN / LARRY SIMKINS: Tim and Larry's 1995 continuation of John's work, has I'm sure, inspired more people than just me, to work on this challenge. Plus, they added another million digits to the total. This had to be a mind numbingly large number in 1995's processor world.

JASON DOUCETTE: Jason started from scratch in 1999. After a total run of 288.8 days, according to the posted numbers on his site, he reached 13,000,000. Truly, an impressive number. I mean think about it for a second. A 1, followed by 12.999999 MILLION 0's!! It is a notepad, text file of 13 MEGABYTES! The number is HUGE!! A job well done Jason!!

ISTVAN BOZSIK: Istvan's calculations actually came after Jason Doucette's. Istvan started in March 2000, compared to Jason's beginning of August 1999. Jason had already long passed 5 million digits, and was already fast approaching 12 million, by the time Istvan reached his conclusion. Istvan eventually went on to 6 million, but if we use the published numbers on the web sites, I can justify the reason Istvan's name appears on this list. His calculating application was FAST!! Compare the notes on the two web sites, and you might notice that Jason used a Pentium II - 266 megahertz machine to calculate to 5 million, and then a 400 megahertz machine, for the rest of his work, while Istvan claims to have only used a 266. Yet, Istvan Bozsik completed 5 million digits in 25.4 days, compared to Mr. Doucette's time of 37.4 days. This will become of higher and higher importance, as the digit length grows! His application allowed me to continue this search from 14 to 29 million digits.

BEN DESPRES: I would like to thank and give credit to Ben for his support. His application set the standard that got quite a few people interested in trying to code a faster 196 app. Ben's is over 3 times faster than Istvan's program. For over 4 months in 2002, Mr. Despres was the King-Of-The-Hill speed champion helping me get from 30 million to 45 million digits. I thank him ever so much for taking the time to write an application for this quest, and for having the programing knowledge to make it so powerful. He listened to a million little requests from me, and implemented the ones that made sense, and pointed out the short falls of the ones that didn't. He has also taken it upon himself to run the search for Lychrel Numbers, and has made a couple amazing discoveries in his work. Maybe I can get most of his stuff organized into a page of it's own, but for now, you can scan the My Blackboard and Blackboard Archive pages for notes on his findings.

ERIC SELLERS: After receiving probably a dozen different apps to test, finally I got one from Eric that was considerably faster than Ben's, and that says a lot!! His app got me from 46 million to 66 million in just over 3 months. I really thank Eric for all he did!

ERIC GOLDSTEIN: As I write this in April of 2005, Eric has had the fastest 196 application on the planet. It's as simple as that. He has spent literally MONTHS (years??) in his fine tuning and optimizing efforts. They have finally paid off in the fact that he has his name on the Milestones page for more milestones than any other coder!! As with everyone else, I owe a great deal of thanks to Eric for his work. His site is http://www.lotendelen.nl.

VAUGHN SUITE: Vaughn has challenged Eric Goldstein to improve faster than any other coder. Vaughn has contributed quite a few comments and ideas to a Mathematical Solution for the 196 quest. My thanks to Vaughn!!

It is an extremely interesting insight at computer processing, in that it took John Walker 3 YEARS to come up with the first million while Tim Irvin and Larry Simkins came up with another million in two months. This is amazing, since each new addition takes a fraction of a second longer to perform. As Mr. Bozsik points out on his web site:

As the number grows from iterations to iteration, it lasts longer and longer to compute the new sum. There is a quadratic relation between the iteration number and the machine cycle needed. As the triangle illustration below shows, (Not shown) there is also a quadratic relation between the digits reached and the machine cycle needed. To reach 2 million digits one must wait 4 times longer than to reach 1 million digits. 6 million digits takes 36 times longer.

It takes longer and longer and longer to produce the numbers. Luckily for us, machines are getting faster and faster!!

Both John and Tim / Larry, used machines that were simply not available to the common household, to produce their results. Now, most people have processors sitting in a closet, collecting dust, that are more powerful (read FASTER) than anything available to them.

Jason talks about using a Pentium II - 266MHz, and a Celeron 400MHz. Much of Ian Peter's work on 196 and his other projects was on an Athlon 500. I am currently running Mr. Goldstein's program on the 196 number using an Intel P4- 2.8 GHz machine with 1GB of RAM. (0-1,000,000 digits in about 5:16.)

Anyone who has ever tried to find a palindromic solution to 196 gets a nod from me, but for the research I've done, the above people belong at the head of the list!!