Mersenne Digest Saturday, July 3 1999 Volume 01 : Number 592 ---------------------------------------------------------------------- Date: Thu, 1 Jul 1999 19:34:04 +0100 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Re: Mersenne: M39 (yes, 39) On 1 Jul 99, at 12:06, Jeff Woods wrote: > Very well -- I will now predict that the NEXT Mersenne prime we find will > be discovered very shortly (within 60 days, sans verification time), and > will be PRECISELY: > > 2^7682383 - 1 If I were a bookie, I'd happily offer you odds of 1000-1 on that prediction. > > I say this only because I have that number reserved, and because it falls > within the subjective "Mersenne Island" that p=6972593 makes possible. > > (If you take the LARGEST Mersennes, M30 and up, and calculate the gap > between them, you will find that the percentage is .8806259 through > .9850544. Thus, if I arbitrarily choose 87% either way from the current > discovery, this gives an "Island" potential (if such exists) of another > prime possibly between p = 6066155 and p = 7879030. I choose to guess > that this is the lower of the two primes in this island, if it exists, > SOLELY because I'm too stink'n proud to think I might have missed out on > the discovery of a WORLD RECORD find. ;-) > My reading of the "island" theory is that the centre of the next "island" should be closer to 6 million than 7 million. Therefore, if "M38" has a mate, the "island" theory predicts that "M38" is the higher of a pair. _If_ a pair exists. _If_ the "island" theory really does hold water. I'd very much like to see the "island" theory proved; however, to the best of my knowledge, there isn't even a half- formed heuristic argument as to why "islands" should exist - it's just an observation of a (statistically insignificant) pattern. There are still plenty of untested exponents in the 6 millions, so there's plenty of opportunity to find another Mersenne prime somewhere amongst them. Also, we aren't sure that there are no Mersenne primes in the high 3 millions, the 4 millions or the low to mid 5 millions; finding one in the "gap" would do the "island theory" serious damage. Irrespective of the "island" theory, I'll predict that exactly one more Mersenne prime will be found with an exponent less than 10 million, but I wouldn't risk more than $10 on a bet at even money odds, or venture to hazard an estimate of the value of its exponent in the event that my prediction turns out to be true. Regards Brian Beesley ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 15:52:14 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Hmmm. Seeing as how anyone with even the most rudimentary of Internet searching skills (i.e. me) can find a publicly available Internet page with a certain highly important number on it, I ask why it is there. I thought that "those in the know" were *absolutely not* supposed to reveal it to anyone until it had been offically disclosed. Publishing an Internet page seems a little odd, you see, because entropia.com/ips and www.mersenne.org still say nothing specific. What do Mr. Woltman and Mr. Kurowski have to say about this? Even though I know M38 and the location of said page, I will not discuss it with anyone until the _official_ announcement has been made. If the general public gets wind of this, it probably will be Not Good (TM), so I'd ask the other members of this list not to say anything until we hear from Woltman or Kurowski. S.T.L. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 1 Jul 1999 22:11:55 +0200 (MET DST) From: [EMAIL PROTECTED] Subject: Re: Mersenne: Hmmm. [EMAIL PROTECTED] writes > Seeing as how anyone with even the most rudimentary of Internet searching > skills (i.e. me) can find a publicly available Internet page with a certain > highly important number on it, I ask why it is there. I thought that "those > in the know" were *absolutely not* supposed to reveal it to anyone until it > had been offically disclosed. Publishing an Internet page seems a little odd, > you see, because entropia.com/ips and www.mersenne.org still say nothing > specific. What do Mr. Woltman and Mr. Kurowski have to say about this? > Even though I know M38 and the location of said page, I will not discuss it > with anyone until the _official_ announcement has been made. If the general > public gets wind of this, it probably will be Not Good (TM), so I'd ask the > other members of this list not to say anything until we hear from Woltman or > Kurowski. Have you double-checked the exponent you found? Perhaps a hacker broke into the web site and is publishing an incorrect exponent. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 01 Jul 1999 17:30:18 -0400 From: Jeff Woods <[EMAIL PROTECTED]> Subject: Re: Mersenne: M39 (yes, 39) At 07:34 PM 7/1/99 +0100, you wrote: >My reading of the "island" theory is that the centre of the next >"island" should be closer to 6 million than 7 million. How so? If indeed p=6972593 is one of a pair in an island, then it is not the middle. It is either the higher or the lower of the two. Since the "pairs" have tended to fall approximately within 0.88 of each other (and sometimes much closer), that means that if M38 is the upper of a pair, p * .88 = 6135881 as the potential "lower bound". If M38 is assumed the lower of a pair in an island, p / .87 = 7923401 as the potential upper bound. There is currently no reason to assume 1) That the Island theory holds or 2) That if it does, that M38 is speifically the higher or the lower of the "pair". I choose to believe that the theory holds, "just because it suits", and that M38 is the LOWER of the pair that will result, again, "just because that still leaves me in the running" for finding a HIGHER number, since I have several machines testing potential numbers in that range. What a selfish reason to believe a mathematical theory, eh? Then again, this is all for fun, so since the money's been won, I want to find a bigger prime, as we all do. ;-) >Therefore, if >"M38" has a mate, the "island" theory predicts that "M38" is the >higher of a pair. How so? We don't know WHICH of the bookends M38 might be... The number that GIMPS recently found MIGHT be M39, with M38 still lurking (or even M40 - -- we haven't exhaustively searched yet). How can you state one way or the other, even IF the island theory holds, which end of the island the new discovery is? > _If_ a pair exists. _If_ the "island" theory really >does hold water. I'd very much like to see the "island" theory >proved; however, to the best of my knowledge, there isn't even a half- >formed heuristic argument as to why "islands" should exist - it's >just an observation of a (statistically insignificant) pattern. Might big ifs, to be sure. However, the larger the "gaps" between the supposed islands become, the more apparent the theory will be -- if the theory holds. If we do find M39 in the range of +/- 10% of M38, it is not conclusive proof of the Island theory, but one more nail to secure the foundation.... I surmise we'll need far more statistical data before we can even talk with reasonable confidence about Island Theory, and even then, we'll lack mathematical/heuristic proof. >There are still plenty of untested exponents in the 6 millions, so >there's plenty of opportunity to find another Mersenne prime >somewhere amongst them. Also, we aren't sure that there are no >Mersenne primes in the high 3 millions, the 4 millions or the low to >mid 5 millions; finding one in the "gap" would do the "island theory" >serious damage. Indeed. I'm predicting there are none, "just because it suits". TO me, this is a much better prediction than the now-disproven "There are exactly 37 Mersenne Primes, no more and no less". ;-) Fun. Just For Fun. Are we having fun yet? Are we there yet? Can I have a drink of water? >Irrespective of the "island" theory, I'll predict that exactly one >more Mersenne prime will be found with an exponent less than 10 >million, but I wouldn't risk more than $10 on a bet at even money >odds, or venture to hazard an estimate of the value of its exponent >in the event that my prediction turns out to be true. I think you are correct, and I think its exponent will be consistent with island theory. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 02 Jul 1999 12:09:18 -0500 From: "Robert G. Wilson v" <[EMAIL PROTECTED]> Subject: Mersenne: Complete Factorization of M16384 This is a multi-part message in MIME format. - --------------78E48C926B5AC9DD37B40DA6 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Et al, This was gathered and cross checked with many sources including the "Cunningham Project" and "The Book of Numbers." The next biggy is to find a factor for F14! You'll be famous. Bob. - --------------78E48C926B5AC9DD37B40DA6 Content-Type: text/plain; charset=iso-8859-1; name="M16384.txt" Content-Transfer-Encoding: quoted-printable Content-Disposition: inline; filename="M16384.txt" The complete factorization (that is all numbers below are prime) of the M= ersenne Number, M16384 =3D 2^2^14 -1, is (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1) = (2^16+1)(2^32+1)(2^64+1)(2^128+1) ... (2^8192+1). For n >1, factors of th= e Fermat Numbers, see above Fn =3D 2^2^n +1, are of the form k*2^(n+2)+1,= k and n are listed below. 1 * 3 1/2,= 0 * 5 1/2,= 1 * 17 1,= 2 * 257 8,= 3 * 65537 1024,= 4 * 641 5,= 5 * 6700417 52347,= 5 * 274177 1071,= 6 * 67280421310721 262814145745,= 6 * 59649589127497217 116503103764643,= 7 * 5704689200685129054721 11141971095088142685,= 7 * 1238926361552897 1209889023954,= 7 * 93461639715357977769163558199606896584051237541638188580280321 k1,= 8 * 2424833 1184,= 9 * 7455602825647884208337395736200454918783366342657 k2,= 9 * 74164006262753080152478714190193747405994078109751902390582131614441575= 9504705008092818711693940737 3640431067210880961102244011816628378312190= 597, 9 * 45592577 11131, = 10 * 6487031809 1583748, = 10 * 4659775785220018543264560743076778192897 1137640582563481089664199400165229051, = 10 * 13043987440548818972748476879650990394660853084161189218689529577683241= 6251471863574140227977573104895898783928842923844831149032913798729088601= 6179460941194490105959067101305319061710183544916096191939124885381160807= 12299672322806217820753127014424577 = k3, 10 * 319489 39, = 11 * 974849 119, = 11 * 167988556341760475137 10253207784531279, = 11 * 3560841906445833920513 434673084282938711, = 11 * 17346244717914755543025897086430977837742184472366408464934701906136357= 9192879108857591038330408837177983810868451546421940712978306134189864280= 8260145427587085892438736855639731189488693991585455066111474202161325570= 1726056413939436694579322096866510895968548270538807264582855415193640191= 2464931182546092879815733057795573358504982279280090942872567591518912118= 6227517143192297881009792510360354969172799126635273587832366471931547770= 9142774537703829458491891759032511093938132248604429857397165071105924446= 2177542540706913047034664643603491382441723306598834177 = k4, 11 * 114689 7, = 12 * 26017793 1588, = 12 * 63766529 3892, = 12 * 190274191361 11613415, = 12 * 1256132134125569 76668221077, = 12 * 22964766349327374158394934836882729742175302138572222575931764391308418= 9516096132382659280380864312315776330453915314460450194556572637889591520= 9595950078110112609649565697614533808432360939124257004959146146100932078= 2551308966824222425528731569111534949127744166427236012769418206949701929= 9146312879536791243280784034435890015447850432092430051766723651249856755= 6601129618233580642646148465607080211504838965935523618206824195034420199= 9449825647341556766313684295383743697537161298411893329950259437024572510= 8495597978690111320115308067310794731449989885761657097352227077484815352= 3682562394459511253374123416009099322199740571184849711562631377061584634= 0179366098118224044157942824481075801501388316794925034549722720218237177= 9894151535731419443909337015329574723107267273040294611920201206671193244= 0906462375814643855500503626564314311613740004222882394574001010576427885= 6096541459650682547836386210032027169896230115182649724551245475912070548= 4184592114074030067691647198697499592224398061647154701759458614628952014= 5321451796076268635556203929630712935725274464512803427346600290020957571= 6007479669129661683944031076099220826572016496603734398963042158832323677= 881589363722322001921 k5, 12 * 2710954639361 , = 13 * 2663848877152141313 20323554055421, = 13 * 3603109844542291969 k6, = 13 * 319546020820551643220672513 609485665932753836099, = 13 0855986463911083746443030121314134290269199710354333548873484605260526373= 3977989359657799060433874643903498948235985904921882492966060510038911758= 2120258754885519585052756213421228476386163579247803563282797040796563182= 4221790536437811269222245732796221914234345197665602841820966957753955466= 6993817222448314606567175117218380212969973586445252294954185203585473433= 7212733863157970031522224970363941209099492883375677993153879701370104382= 7441935382568667381523475316871728376003680482940175414197261177180757890= 1305085034511262453455544240829435374979385563369194362528910727438968217= 0660447227313276738663511996400570534245795710526003680482940175414197261= 1771807578901305085034511262453455544240829435374979385563369194362528910= 7274389682170660447227313276738663511996400570534245795710520391440263888= 9064382864987765343240332925550930017192143468703628304999985059646548483= 1745312837784306095424925969824805774392718346190010555731278561491488640= 8687150037674036406375138263918549781974774518229655227674646917077478578= 2604677338131683907661063093685741813111168096285019490413360405743657216= 6380793143121164022082315774528928640686372250989238437453446230287893029= 3216249248020864193524835645666567040322357082663479441563991600850223287= 9355149141446622157183268341260950665476845850593126292672285108878441780= 7929803884823075735231345620938363014246275087163690858400334618668871153= 3231889535016445390490581465226508042082188768521912384471154876904586555= 0497148053267518010393454599197212179695074532337789302978167311885477351= 0343692766955559035084698356992267297834672203318171938778380373913254412= 1412443776132558830773620439200314632495528294603756672037742853587398416= 1942480391232235552342417767374816991000869484836290575215308122955018045= 7461818177116273107991568023913421050712328185424870586243647386645716894= 4009173876208484146658062283764966523697395543539785704707917818059490244= 0772876565000572481849846211069652060751185774024009365138945603106474516= 4075177456473622024173117880785704073275043542142058330939627443903981692= 8054815441064465334828437766901084751902017441876082532781100516755656294= 8062313033701884413100193693299508399443471053029166862979957167301699984= 2502691205393017153443382350875118979353824315989818432973345744056138883= 6952719290470687795279598211653785553186682843653266109712561937642303380= 5285066214685326018568501334396163929771111985638342657 k7, 13. - --------------78E48C926B5AC9DD37B40DA6 Content-Type: text/x-vcard; charset=us-ascii; name="rgwv.vcf" Content-Transfer-Encoding: 7bit Content-Description: Card for Robert G. Wilson v Content-Disposition: attachment; filename="rgwv.vcf" begin:vcard n:Wilson v;Robert G. tel;cell:316-393-6353 tel;fax:316-262-7221 tel;home:316-788-8757 tel;work:316-264-6353 x-mozilla-html:FALSE org:Kansas Paint & Color Co., Inc. adr:;;132 N. Mosley;Wichita;KS;67202-2898; version:2.1 email;internet:[EMAIL PROTECTED] title:President fn:Robert G. Wilson v end:vcard - --------------78E48C926B5AC9DD37B40DA6-- ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Sat, 3 Jul 1999 15:01:13 -0400 From: "Geoffrey Faivre-Malloy" <[EMAIL PROTECTED]> Subject: Mersenne: Prime95 and speed Has anyone else noticed Prime95 executing at twice the speed while factoring then slowing down when it gets to a certain point in the factoring process? Let me clarify a bit more...I have a PII500 that while working on a factor for M9899041 does about .050 seconds per iteration. I've noticed that it does about .029 seconds per iteration when it is factoring through 1069176222*2. Is there some reason why there would be such a huge difference in speed after that point? I've done the usual things - make sure nothing else is running, run WinTop, etc. Prime95 is getting nearly 100% of the CPU power all the time. G-Man ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ End of Mersenne Digest V1 #592 ******************************
