Re: Mersenne: M38 = M6972593
I'm curious - had this already been tested by someone else using the defective v17 software? Randy Given [EMAIL PROTECTED] http://members.aol.com/GivenRandy public key at http://members.aol.com/GivenRandy/pgpkey.asc Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: M38 = M6972593
At 07:19 05.07.99 -0400, [EMAIL PROTECTED] wrote: I'm curious - had this already been tested by someone else using the defective v17 software? No. /* Steinar */ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re; Mersenne: Lehmer question
Let Mp = 2^p - 1 be a Mersenne prime, where p 2. Denote S[1] = 4 and S[k+1] = S[k]^2 - 2 for k = 1. Then S[p-2] == +- 2^((p+1)/2) mod Mp. Predict which congruence occurs. Dear Peter and All, This is as far as I can go in Ubasic: p Result 3 + 5 + 7 - 13 + 17 - 19 - 31 + 61 + 89 - 107 - 127 + 521 - 607 - 1279 - 2203 + 2281 - 3217 - 4253 + The algebra suggests two values to consider 1) Consider q=((p+1)/2) mod n Taking the p pairwise where signs differ eliminates the following possible n: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27, 28,29,30,32,33,34,35,36,37,38,39,40,42,43,45,46,47,48,49,51,52,54,55,57, 58,59,60,61,63,64,66,67,72,73,74,75,77,78,80,81,84,86,87,89,91,96,99,103, 104,111,114,115,120,122,125,126,127,129,131,133,144,146,151,154,156,162, 169,177,178,182,183,185,189,192,193,197,203,208,211,222,225,230,231,240, 245,254,258,259,262,263,266,267,273,288,297,301,302,309,311,312,319,347, 353,359,364,366,370,375,378,399,462,493,507,515,518,524,526,531,534,546, 549,555,567,569,576,609,622,624,633,637,638,691,694,706,789,798,801,803, 841,933,986,1041,1048,1057,1059,1077,1092,1093,1098,1110,1125,1134,1138, 1139,1487,1545,1578,1593,1602,1606,1607,1823,1866,2073,2082,2117,2118, 2123 That first gap at 31 is interesting... Conjecture: take ((p+1)/2) mod 31 if in (0,2,3,7,16,17,19) then sign(S[p-2]) = + if in (4,9,10,13,14,20,23,25,28) then sign(S[p-2]) = - if in (1,5,6,8,11,12,15,18,21,22,24,26,27,29,30,31) then no data 2) Consider q=(p-2) mod n Taking the p pairwise where signs differ eliminates the following possible n: 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27, 28,29,30,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,52,54, 55,56,57,58,59,60,61,63,64,66,67,68,70,72,73,74,75,76,77,78,80,81,84,86, 87,89,90,91,92,94,96,98,99,102,103,104,108,110,111,114,115,116,118,120, 122,125,126,127,128,129,131,132,133,134,144,146,148,150,151,154,156,160, 162,168,169,172,174,177,178,182,183,185,189,192,193,197,198,203,206,208, 211,222,225,228,230,231,240,244,245,250,252,254,258,259,262,263,266,267, 273,288,292,297,301,302,308,309,311,312,319,324,338,347,353,354,356,359, 364,366,370,375,378,384,386,394,399,406,416,422,444,450,460,462,480,490, 493,507,508,515,516,518,524,526,531,532,534,546,549,555,567,569,576,594, 602,604,609,618,622,624,633,637,638,691,694,706,718,728,732,740,750,756, 789,798,801,803,841,924,933,986,1014,1030,1036,1041,1048,1052,1057,1059, 1062,1068,1077,1092,1093,1098,1110,1125,1134,1138,1139,1152,1218,1244, 1248,1266,1274,1276,1382,1388,1412,1487,1545,1578,1593,1596,1602,1606, 1607,1682,1823,1866,1972,2073,2082,2096,2114,2117,2118,2123,2154,2184, 2186,2196,2220,2250,2268,2276,2278,2974,3090,3156,3186,3204,3212,3214, 3646,3732,4146,4164,4234,4236,4246 Again a gap at n=31 Conjecture: take (p-2) mod 31 if in (0,1,3,4,11,28,29) then sign(S[p-2]) = + if in (5,6,12,15,16,17,22,23,25) then sign(S[p-2]) = - if in (2,7,8,9,10,13,14,18,19,20,21,24,26,27,30,31) then no data It's all a bit thin and arm-waving, but I would be interested to see if a continuation of the series confirms or denies either of these conjectures. Regards, Andy Steward Factorisations of generalised repunits at: http://www.users.globalnet.co.uk/~aads/index.html Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Re: Mersenne: Lehmer question
Dear All, Following up my own msg here. First, there is an obvious linear relationship between my two conjectures, so they are equivalent. Second, predictions where possible (U=Unknown): p (p+1)/2 mod 31 Conj 1 (p-2) mod 31 Conj 2 4423 11 U 19 U 9689 9 - 15 - 9941 11 U 19 U 11213 27 U 20 U 19937 18 U 2 U 21701 1 U 30 U 23209 11 U 19 U 44497 22 U 10 U 86243 1 U 30 U 110503 10 - 17 - 132049 26 U 18 U 216091 11 U 19 U 756839 3 + 3 + 859433 26 U 18 U 1257787 28 - 22 - 1398269 23 - 12 - 2976221 18 U 2 U 3021377 28 - 22 - 6972593 6 U 9 U Regards, Andy Steward Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Digest V1 #593
Mersenne Digest Monday, July 5 1999 Volume 01 : Number 593 -- Date: Sat, 03 Jul 1999 13:57:08 -0700 From: Eric Hahn [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? Actually, the point is closer to 107350*2^32, and yes the change is normal. It happens after the program gets through the trial factors up to 2^62. After it reaches the upper limit of 2^64 (approx. 429000*2^32), it goes back down. It's partially a result of the fact that there are many more trial factors to test between 2^62 and 2^64. 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. Again, it's normal. You'll probably notice the iteration time at a ratio of 9/5 for the higher range (2^62 - 2^64) of trial factors... Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sat, 3 Jul 1999 20:10:58 -0400 (EDT) From: "David A. Miller" [EMAIL PROTECTED] Subject: Mersenne: mersenne.org not available I haven't been able to get a response from mersenne.org for a couple of days. Is something wrong over there? David A. Miller Rumors of my existence have been greatly exaggerated. Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sun, 4 Jul 1999 17:48:22 -0400 From: "Geoffrey Faivre-Malloy" [EMAIL PROTECTED] Subject: Mersenne: Estimates to finishing up to 2050??? Has anyone calculated (given the current rate of growth) how long it will take to do 1st level LL tests up to 20 million? G-Man Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sun, 4 Jul 1999 18:27:26 -0400 (EDT) From: Lucas Wiman [EMAIL PROTECTED] Subject: Re: Mersenne: More on the FAQ Chris, on your website http://www.utm.edu/research/primes/notes/faq/NextMersenne.html, you say: "This means that the geometric mean of two successive mersenne exponents is 2 raised to 1/e^gamma or about 1.47576." The definition of geometric mean of two numbers a and b is: sqrt(a*b) Therefore the geometric mean must be between a and b. I think that you mean that the geometric mean of two successive mersenne numbers is 2 raised to the (1/e^gamma) raised to the index of the mersenne numbers. - -Lucas Wiman Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sun, 04 Jul 1999 19:17:36 -0700 From: Spike Jones [EMAIL PROTECTED] Subject: Mersenne: how long to 20.5M Geoffrey Faivre-Malloy wrote: Has anyone calculated (given the current rate of growth) how long it will take to do 1st level LL tests up to 20 million? Gman, I extrapolated and posted an estimate of April 2007, back in February of this year. If I take a linear model starting 1 Jan 99, I get August 2005. If I use the latest curve fit suggest on the wicked-cool site: http://entropia.com/ips/stats.html I get September 2004. For my newest prediction, I split the difference and estimate spring 2005. spike Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm -- Date: Sun, 04 Jul 1999 22:15:38 -0400 From: George Woltman [EMAIL PROTECTED] Subject: Mersenne: M38 = M6972593 Hi all, As the newspaper should announce the new prime on Monday or Tuesday, I've placed the info on the new prime at http://www.mersenne.org/prime.htm Congratulations to Nayan Hajratwala and all GIMPS members for our fourth success! Each Mersenne announcement is different. This time round I finally figured out how to get the press interested in the new number - tell them its a secret. The Oregonian was doing an article on Richard Crandall and when the found out there was a new prime and we wouldn't tell them what it was, their interest level went way up! I admire the resourcefulness of GIMPS members for going on a "scavenger hunt" and finding out the exponent a few days before this email was sent out. However the resourcefulness award must go to one enterprising GIMPS member that dug through all the
Mersenne: IPS Factoring Assignments
I was just about going to ask if George was going to more factoring assignments available to IPS or if IPS just wasn't showing ones that had been made availabe, when I noticed that the range of 10.0 - 10.2 Mil was posted. Now instead of having enough for about 2 weeks, there are enough for about 7 weeks, since GIMPS members go through them at a rate of ~1000 per week Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
Mersenne: M38 = M6972593
(Note to Scott - create a dummy non-zero residue a stick it in the cleared exponents report). Too late!! The Cleared Exponents Report reads: 6972593 62 P 0x 01-Jun-99 13:57 nayan precision-mm Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm
