Mersenne Digest Monday, July 5 1999 Volume 01 : Number 593
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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 1073500000*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. 4290000000*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...
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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.
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Date: Sun, 4 Jul 1999 17:48:22 -0400
From: "Geoffrey Faivre-Malloy" <[EMAIL PROTECTED]>
Subject: Mersenne: Estimates to finishing up to 20500000???
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
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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
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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
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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 cleared and assigned
exponent lists and human-readable files and deduced the exponent in early
June! (Note to Scott - create a dummy non-zero residue a stick it
in the cleared exponents report).
Good luck to all in the search for M39!
Have fun,
George
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Date: Mon, 5 Jul 1999 06:34:14 +0200 (MET DST)
From: [EMAIL PROTECTED]
Subject: Mersenne: Lehmer question
Problem A3 in Richard Guy's `Unsolved Problems in Number Theory'
includes this question, by D.H. Lehmer:
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.
For example, when p = 3, S[1] = 4 == 2^2 (mod 7).
When p = 5, S[3] = 194 == 2^3 (mod 31).
When p = 7, S[5] = 1416317954 == -2^4 (mod 127).
The sign is + for p = 3 and p = 5 but - for p = 7.
Do we have the pattern through M38?
Peter Montgomery
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Date: Mon, 5 Jul 1999 07:19:11 EDT
From: [EMAIL PROTECTED]
Subject: 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
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Date: Mon, 05 Jul 1999 13:33:31 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: 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 */
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Date: Mon, 5 Jul 1999 18:39:44 +0100
From: "Andy Steward" <[EMAIL PROTECTED]>
Subject: 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>
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Date: Sun, 04 Jul 1999 18:16:17 -0700
From: Eric Hahn <[EMAIL PROTECTED]>
Subject: Mersenne: Mersenne M38
>On Mon, Jun 28, 1999 at 07:45:11PM -0700, Eric Hahn wrote:
>>It hasn't been announced yet... but from what little information
>>that is available, i.e. The Oregonian newspaper article, the
>>exponent must be =at least= 6,643,859.
>Hmmm, my guess was at about 6,2 million, but nobody else guessed,
>so there :-)
Actually, now that the exponent for M38 is known, I can say
that I had narrowed it down to 5 candidates (7 before the
Oregonian article). They were:
5,750,881 6,382,513 6,836,327 6,972,593
7,143,163 7,213,391 7,310,981
These were the only exponents that were no longer being
worked on in one form or another, and was not listed on the
cleared exponents list, for that time frame...
I determined this from the statistics I've been tracking
for a while now. Part of which I've now posted to my website
at ( http://www.mcn.org/2/ehahn/netforce/ips-stats.html ).
I'll be posting more as I get them reformatted to look better...
Eric
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Date: Tue, 6 Jul 1999 00:47:05 +0100
From: "Andy Steward" <[EMAIL PROTECTED]>
Subject: 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
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End of Mersenne Digest V1 #593
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