If more people are working on the 196 quest, I thought I would provide a location for someone to come to and verify the numbers that they have found. If yours and mine don't match, LET ME KNOW!!
Eric Goldstein has pointed out that some of the files are not the first iteration of the dataset. (See the Blackboard entry for 8/6/02) For example, the 2,000,244 and 14,000,008 files shown below are in fact, the second iteration of each. I originally thought that all of these files were the first iteration to contain the stated digit length, but I guess not... I do still believe that they are all correct for the given iteration!!
In addition, Beth Cooper and Chun Yi asked to see the spreadsheet that I mentioned somewhere on the site, that I use to track the status of my progress. I don't know if anyone else is interested, and I don't even know what value it could be to someone, but here it is in a zipped Excel file. Maybe there is value to people like Eric Goldstein, who was verifying some of my work, by running 196 also. I don't intend to update it except maybe rarely, but it is current as of this afternoon (10/7/04). Anyway..... It is there if someone wants it. If nothing else, it shows a really nice "timeline" of how I have moved forward!!
Towards the bottom of the page, is a prgoram that you can download, that was written by Ben Despres. With some formatting, you can load your number into his program, and verify that any iteration you are on, is giving you the correct answer.
Here are the first 25 digits of every data file that I have..... I hope it is useful to someone. :-)NOTE: As I've fallen behind in updates, this page has gotten a bit burdensome to keep updated. In addition, I really don't think adding every milestone's data is of any use to anyone, since I don't know of anyone duplicating my work this far out. As a result, I've discontinued keeping it totally current. If someone decideds that they really need to know the first 25 digits of a dataset not listed here, let me know, and I will email you the information directly. I'm sure everyone understands.
| Digit Count | Iteration Count | First 25 |
1,000,000 2,000,000 2,000,244 3,000,000 4,000,000 5,000,000 6,000,000 7,000,000 8,000,000 9,000,000 10,000,000 11,000,000 12,000,000 13,000,000 14,000,000 14,000,008 15,000,000 16,000,000 17,000,000 18,000,000 19,000,000 20,000,000 21,000,000 22,000,000 23,000,000 24,000,000 25,000,000 26,000,000 27,000,000 28,000,000 29,000,000 30,000,000 31,000,000 32,000,000 33,000,000 34,000,000 35,000,000 36,000,000 37,000,000 38,000,000 39,000,000 40,000,000 41,000,000 41,388,546 42,000,000 43,000,000 44,000,000 44,444,444 45,000,000 46,000,000 47,000,000 48,000,000 49,000,000 50,000,000 51,000,000 51,737,154 52,000,000 53,000,000 54,000,000 55,000,000 56,000,000 57,000,000 58,000,000 59,000,000 60,000,000 61,000,000 62,000,000 62,086,375 63,000,000 64,000,000 65,000,000 66,000,000 67,000,000 68,000,000 69,000,000 70,000,000 71,000,000 72,000,000 72,433,237 73,000,000 74,000,000 75,000,000 76,000,000 77,000,000 78,000,000 79,000,000 80,000,000 81,000,000 82,000,000 83,000,000 84,000,000 85,000,000 86,000,000 87,000,000 88,000,000 89,000,000 90,000,000 91,000,000 92,000,000 93,000,000 94,000,000 95,000,000 96,000,000 97,000,000 98,000,000 99,000,000 100,000,000 101,000,000 102,000,000 103,000,000 104,000,000 105,000,000 106,000,000 107,000,000 108,000,000 109,000,000 110,000,000 111,000,000 112,000,000 113,000,000 114,000,000 115,000,000 116,000,000 117,000,000 118,000,000 119,000,000 120,000,000 121,000,000 122,000,000 123,000,000 124,000,000 125,000,000 126,000,000 127,000,000 128,000,000 129,000,000 130,000,000 131,000,000 132,000,000 133,000,000 134,000,000 135,000,000 136,000,000 137,000,000 138,000,000 139,000,000 140,000,000 141,000,000 142,000,000 143,000,000 144,000,000 145,000,000 146,000,000 147,000,000 148,000,000 149,000,000 150,000,000 151,000,000 152,000,000 153,000,000 154,000,000 155,000,000 156,000,000 157,000,000 158,000,000 159,000,000 160,000,000 161,000,000 162,000,000 163,000,000 164,000,000 165,000,000 166,000,000 167,000,000 168,000,000 169,000,000 170,000,000 171,000,000 172,000,000 173,000,000 174,000,000 175,000,000 176,000,000 177,000,000 178,000,000 179,000,000 180,000,000 181,000,000 182,000,000 183,000,000 184,000,000 185,000,000 186,000,000 187,000,000 188,000,000 189,000,000 190,000,000 191,000,000 192,000,000 193,000,000 194,000,000 195,000,000 196,000,000 197,000,000 198,000,000 199,000,000 200,000,000 201,000,000 202,000,000 203,000,000 204,000,000 205,000,000 206,000,000 206,967,875 207,000,000 208,000,000 209,000,000 210,000,000 211,000,000 212,000,000 213,000,000 214,000,000 215,000,000 216,000,000 217,000,000 218,000,000 219,000,000 220,000,000 221,000,000 222,000,000 223,000,000 224,000,000 225,000,000 226,000,000 227,000,000 228,000,000 229,000,000 230,000,000 231,000,000 232,000,000 233,000,000 234,000,000 235,000,000 |
2,415,836 4,830,292 4,830,868 7,245,928 9,662,071 12,078,865 14,495,294 16,911,863 19,327,667 21,744,278 24,159,531 26,574,642 28,991,159 31,408,295 33,824,775 33,824,793 36,240,602 38,655,227 41,070,365 43,487,182 45,901,512 48,316,988 50,732,545 53,148,015 55,565,809 57,982,436 60,398,130 62,816,046 65,231,462 67,648,377 70,067,270 72,482,579 74,899,358 77,314,955 79,731,034 82,145,364 84,563,227 86,979,674 89,397,247 91,812,894 94,228,899 96,645,213 99,061,141 100,000,000 101,476,346 103,893,138 106,309,010 107,382,665 108,723,539 111,138,308 113,554,695 115,969,543 118,387,016 120,802,305 123,218,044 125,000,000 125,634,154 128,050,160 130,463,975 132,880,223 135,295,252 137,712,060 140,128,242 142,544,153 144,958,406 147,375,122 149,790,895 150,000,000 152,207,835 154,623,289 157,038,002 159,455,103 161,871,411 164,287,044 166,704,687 169,121,766 171,538,507 173,953,453 175,000,000 176,368,856 178,784,747 181,199,797 183,616,094 186,032,643 188,447,228 190,862,368 193,277,613 195,693,825 198,109,015 200,524,477 202,939,323 205,355,672 207,771,197 210,186,316 212,602,940 215,018,872 217,433,686 219,850,418 222,266,315 224,680,750 227,095,084 229,512,704 231,928,518 234,344,371 236,759,404 239,175,318 241,590,277 244,006,839 246,423,282 248,840,359 251,254,880 253,670,404 256,084,270 258,498,530 260,914,435 263,328,945 265,745,475 268,160,697 270,575,863 272,991,794 275,405,890 277,820,730 280,236,256 282,651,618 285,066,604 287,481,429 289,896,907 292,311,641 294,727,521 297,143,533 299,557,657 301,974,027 304,389,137 306,805,299 309,221,256 311,637,141 314,052,527 316,468,413 318,884,030 321,299,093 323,715,600 326,131,076 328,547,998 330,963,887 333,379,370 335,795,486 338,210,775 340,626,948 343,043,659 345,459,815 347,875,673 350,292,487 352,708,290 355,125,177 357,540,909 359,956,876 362,372,813 364,788,891 367,204,161 369,619,640 372,035,743 374,450,389 376,866,208 379,281,305 381,697,126 384,113,355 386,529,610 388,944,754 391,360,944 393,776,305 396,192,233 398,607,648 401,023,403 403,439,651 405,856,956 408,272,435 410,688,792 413,104,065 415,517,439 417,933,403 420,349,873 422,765,244 425,181,055 427,599,027 430,016,536 432,433,414 434,849,911 437,267,293 439,682,132 442,097,346 444,512,168 446,927,453 449,343,164 449,343,164 454,174,655 456,588,593 459,004,983 461,419,218 463,835,090 466,250,388 468,667,675 471,085,391 473,503,339 475,919,151 478,335,425 480,750,860 483,166,859 485,581,911 487,996,904 490,413,021 492,829,843 495,245,922 497,662,056 500,000,000 500,077,852 502,495,484 504,913,664 507,329,950 509,745,400 512,162,233 514,577,796 516,992,665 519,408,582 521,825,691 524,242,175 526,658,409 529,075,350 531,491,865 533,907,350 536,322,341 538,737,263 541,153,446 543,569,184 545,986,095 548,402,519 550,818,415 553,233,019 555,650,203 558,065,511 560,480,471 562,896,706 565,311,914 In Work |
1321620866345900792403087 1771479103435526006981020 4966682241339127981797944 1572127370436337959801040 1189951505503730299942650 1786916673224171246235654 1717694931286918098671266 1370104827081045647878991 1019762622265770924957665 1877698672190182856774072 1570638871513424055539043 1552863515777339147880472 1094658057189398961997993 1570104209676429293120872 1760057992641613493083452 4479163772166847272965861 1031240279852766564723228 1765950614893173230506692 1326956429587373980563323 1023601015155152788222220 1061077962735256900716595 1055357468774267123532056 1366299557692634038868234 1618818677775920355359715 1314877753155237116425525 1011377187109780706245147 1090994049526433659630228 1117977825788778867038244 1076857885074947084574730 1823526487861564244724874 1751451457695893086640504 7983997334581381745393030 1782282447580070383893664 1758023338115480171010379 1191494564496990603108460 1776180000353277502063208 9667719580493752405737223 1260718990353737727166287 1713947301231045001039844 1083367793408406027652822 1723587855017460734098176 1796080271215504475068003 1312344045189134863351509 9974438904743885498437291 1323537379287526648818853 1435691352112910044161238 1782430225531195634814511 1834222638993065199417095 1754201184575564515873759 1031943459984297079060569 1714140231595266216147023 1027319277035757930071344 1682327227245818701228607 1132236530787968938016671 7189775322254585819022781 1407502882820027975246439 1328004039944465751897404 1359977662868610427305071 1881923366313273415179428 1033298508834332407949161 1753668819826260460568993 1618620689808652775577199 1775871269524132894299290 1609879637228067420870014 1960882487804145715718858 1727971809395357592464645 1715004244814853908992584 1642624515892626147533628 1776989222706458077880113 1051257477717223642530126 1780395318130583334332747 1511850227165859502646376 1595889760479982515515654 1771960332000080473579801 1757016083265992389585326 1315049565144120454520311 1809597642702333754908891 1015802779684755714656655 1316559584457038932346512 1632106585426253096555012 1986111000106825979146786 1008705138345884691746272 1198699207272219566300138 1352672193204568014634580 1776756206228864215556798 1721124162365259992368277 1276307469099717799141965 1808312984821215632848674 1012480217638681141201751 1319596114795897939644010 1475989142103872062172123 1751939135396043222508585 1838830663332309393661252 1776793449035037308767206 1763659752403662711071184 1175499636497806735606789 1315668188291812932328716 1818340855113748165713548 1028371706886347137074883 1440330481696796849948050 1046866858222464987946767 1766913757711631595955714 1368479950294739386391187 1362828111646940179935559 1881507588454484016602013 1032406741781114441023479 1768299281546132721740051 1592228315604702996112807 1032307672289521340027980 1728363664385978446379558 1371628576057332728611441 1408171282423797037195446 1010961355482533511759009 1775655571279791294879229 1034968781871203163914679 1834854968067461127800545 1276319349159512469971672 1636030357158473358172278 1778781020534052343845183 1776694520310345481883637 1838339385684762471833877 1062513163198909662417864 1342599540844045251109166 1726560261621573127603656 1065645149596777550426168 1369987370648582204968231 1364754677893412956617791 1077725969274592498575304 1021367585335991684990409 1357593504958409900797997 1764378472069655752133500 1884349195617554876361307 1814691856257280526407595 1309531209941831133045217 1189989613884366553921768 1395051195770820383642774 1771135333660318106892108 1778391702927079758653571 1012725947322424967634762 1121041007140108077870210 1847779323392555637004235 1280083196671448796316209 1729238936136697427548393 1597118719384752284695424 1774619990337551728717581 1617678254614088001034677 1644699407125444079404186 1327486016146262830536853 1327710752846177644901575 1596411840598771306167516 1730214275086980347571340 1718265558795616271668352 1312106668717122045265595 1767142633789771140100238 1600598556023084120548792 1642997003809356893180691 1314637152473183654990226 1188332537874075530304529 1073006369604535918485472 1859555702340902960335797 1760875634779847532377788 1771357398392101622859349 1023524464013606297309847 1142611035475515082947139 1638277710993139992025743 1142471351629698087522809 1681205753431630755947393 1025169762868649578809387 1056390811637837662190790 1818281510468184428404022 1017374370556308805985779 1992009903767606779381369 1329054188054981518112269 1316910951280828179910916 1327045841005308772401100 1076970507213999804808448 1321151759791130796049814 1198549725898726826143301 1325272168128847516405635 1589743019357954569195326 1790003513535215165183808 1312399913323475917294279 1769432898013976506388766 1818626607326632254471135 1326521712418739845238528 1756008571102755130842700 1080033386138916259428564 1329090739338784333341325 1133666960819913715481109 1387429023786513990346910 1321031053840463298205400 1841359440807157555745530 1436621873243350049254447 1760077886420128171435125 1645558013977187718195235 1634325347132490436204748 1343550229273330059631588 1059776527743508311624176 1050534741172605814636542 1029883359151196593470782 1778455050891958552858248 1099325204644556770554785 1153735022700273560598532 1724946300386006686906998 1714396635836795679955072 1331657446855898449041806 1799071225594998429967931 1108284260244640194542287 1196020372202958470929067 1046351701504472273576819 1644462350518600021444956 1646167982208731045769174 1877755165049243939821476 8918589423163331686495122 1797488733775233079132274 1744941635998996581169339 1792907222802001951438933 1771175645046732089097139 1843704293845284058481146 1982904778200990006745751 1846165739251682244770519 1512971247633930532350888 1725317666128036787316284 1360831732483998591800659 1816927139005667363497058 1561620443180033117533292 1319808959325670088638232 1634273529758445307189566 1110877014860707713184428 1135599357769221630012377 1314487905309579712064310 1776752824611635706720478 1386065459714198997653566 1752395420852108596738179 1014834823371790173254625 1016277544726554817059913 1019406864798804620082115 1706148909500958140200122 1844448649515508246479390 1192405340671479434412558 1778095873670909753059975 1370675801717563608722225 In Work |
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CHECKER APPLICATION FROM BEN DESPRES
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The file that you can download here is a program that Ben Despres wrote. It runs under windows. When it starts, it will display a file select window, where you can choose which file it is, that you want to check. It's easy enough, even for me.... :-)
He has included a text file with the zip, that goes into some detail of how his program works. I think the descriptions below are a faithful paraphrase of his text file, but if anyone finds a discrepancy between what is here, and what is on the text file with the program, trust the text file, NOT my writeup!! :-)
It works with numbers other than 196. I have tested it on my 879, 1997, 7059, 10553, 10563, 32419, 36973, 43844 files. Turns out that my five million digit 7059 file is wrong. :-( O well......
His MOD-9 discovery is something like this:
I discovered a really neat fact about the checksums of the digits generated by flip-and-add... At any given step, the checksum of the result will equal twice the checksum of the last result minus a multiple of nine (that multiple just happens to equal the number of carries). At first I thought this may lead to a "proof" of Lychrelness, but I have given up that idea for now. *BUT*, it *does* lead to a really simple check of whether or not a given number could have resulted on a given iteration, including in some cases whether or not a number could ever have resulted from a given starting number.
Basically, if Cx equals the MOD-9 sum at iteration X, with C0 meaning the same for the starting value:
Actually, three distinct cycles exist, with only the longest using MOD 6... {0}, {3,6}, and {1,2,4,8,7,5}. 196 itself has the longest of those cycles (and no, unfortunately I could not find any patterns between cycle and converging-vs-conconverging).
So, although the CRC will only detect *new* errors, the MOD-9 checksum will (possibly) detect errors that have already occured.
A couple of notes:
His application is written to look at a file which has been formatted in what has become known as "Istvan-Standard Formatting". :-) Anyway, the file should be in a format that looks like this:
Automatic save #12345 (CRC, optional, but there must be a number on position 17)
Initial value: 196 (number must begin on position 19)
Iteration: 2415836 (number must begin on position 19)
Number of digits: 1000000 (number must begin on position 19)
1321620866345900792403087149937072597108944871590062627103371677853101
0218789552032457507537977475995640190839955855884253327321850902244094
0920987126363322689017611006006500875888569961960897043759484747753087
......
The automatic save line: If I understand correctly, there MUST be a number on that line, starting on position 17. My thanks to Eric Goldstein for figuring this out. His app was generating the correct numbers, but his files were failing Ben's Checker program. This was why...
The initial value line is obviously just that. What number did you start with? 196, 879, 1997 etc. This will be used by the program for it's calculations. The number MUST begin on position 19.
The Iteration and Digits line are also used by the program to test the data. The number MUST begin on position 19.
The data itself is 70 characters wide, followed by an End of Line. This makes the file much nicer to look at, even if it adds little or no value. It was what Istvan decided on, and Ben's program used Istvan's formatting. (Hence the name "Istvan-Standard Formatting".) :-) He's pretty sure that nothing bad will happen to the file if you do not format it like the one above, but he is sure that it will crash in an interesting, unexpected way. My opinion is to watch out, and test a backup copy of the file!!
So far, the worst thing I have seen is a message that says the number generated is not correct, even though it is.
Any file not generated by Ben's program, (which is just about anything anyone else has!!) will always get a message that reads something like this:
In Ben's own words: I use a non-mirrored, non-reflected, 0XFFFF-in with no XOR-out, standard CRC-16 with a generator polynomial of 0x1021, in case anyone really needs to duplicate my numbers. That's part of his internal checking for the files written by his application. It's O.K. if this warning appears. In fact, you should expect it.
Then it will report on the actual length compared to reported length. (These two numbers should match!! :-) )
Then, if all is good, you will get a message that reads:
If not, it will read something like what I saw with some of my own previous files:
Ben's app will also display a "waterfall" image of the number, as well as some interesting statistic information about the number. I'm not going to go into it all here. Grab his file if you're interested.
