Complete testing of range at ~42 Million

wackyeh · 2003-02-28, 08:28

The following range is being worked on in every manner (except ECM)...

41,976,841 - 42,057,331

Currently... All exponents have been trial-factored thru 2^64... and are continuing on thru 2^69...

Many of these esponents have also have P-1 done on them... higher than the standard Prime95 calculated limits...

L-L tests are currently running on a number of these exponents as well...

Due to the memory requirements (384MB)... the number of curves that would need to be tested (300 minimum)... and the time it would take for each curve... ECM is currently not feasible... (maybe when the P7 at 10GHz using SSE6 is around)...

Eric

wackyeh · 2003-02-28, 22:52

It has come to my attention that there has been interest in doing testing of exponents in the range that was predicted for the first 10 million digit Mersenne prime... of which I had made the "prediction"... a full 16 months before 2^13,466,917 was actually found...

I have reserved the range listed above (41976841 - 42057331) thru George... and have been working on it... since before 2^13,466,917 was discovered... There are currently 15 machines tasked with this range... performing trial-factoring, P-1 and L-L testing... and an additional 6 preparing to start being tasked... Most are high-end machines...

Anybody wishing to trial-factor, P-1 and/or L-L test the larger part of the predicted range (41,564,021 - 41,976,829 and 42,057,373 - 42,516373) is more than welcome to have at it... but as I have posted to the Mersenne mailing list... and the Yahoo list (now defunct)... there are NO guarantees or warranties offered up... Testing is at your own risk... of both success AND failure...

Eric

Thomas11 · 2003-03-05, 18:13

I would like to participate the search in that range.
So I will start trial factoring in the lower range (41,564,021 - 41,976,829) up to 2^60 as a first step.
Is that alright?

Thomas.

Thomas11 · 2003-03-05, 18:29

Eric,

I've read your posting at
http://www.mail-archive.com/mersenne@base.com/msg05046.html

Now I have just a few questions:
Is there some information available on the predictid ranges for M#41 and/or M#42?
And what's known about M#44 and higher ones? Is there a prediction on how many Mersenne-Primes will or may be in the GIMPS range up to M79300000?

Thomas. :?

wackyeh · 2003-03-05, 21:59

Quote:

Originally Posted by Thomas11

I would like to participate the search in that range.
So I will start trial factoring in the lower range (41,564,021 - 41,976,829) up to 2^60 as a first step.
Is that alright?

Thomas.

Fine with me... :-) Nobody else seems to have claimed that range... so have at it... :-)

Eric

wackyeh · 2003-03-05, 22:51

Quote:

Originally Posted by Thomas11

Eric,

I've read your posting at
http://www.mail-archive.com/mersenne@base.com/msg05046.html

Now I have just a few questions:
Is there some information available on the predictid ranges for M#41 and/or M#42?
And what's known about M#44 and higher ones? Is there a prediction on how many Mersenne-Primes will or may be in the GIMPS range up to M79300000?

Thomas. :?

Thomas,

Wouldn't you know... I can't find my notes on this info... :-( I will have to try and look harder for them.... Just another thing I've lost around here... ;)

Until I do... as my memory serves... there was 44 Mersenne Primes predicted up to 79.3 million... M#41 somewhere around 18 million IIRC... M#42 was just under 10 million digits... at like around 31 million... and M#44 somewhere up at about 56/57 million... IIRC... M#45 was past GIMPS range as like 84 (or 94??) million...

There was also info on M(100 million digits) and M(1 billion digits)... but those were more sticky... and less reliable... because of the lack of sufficient data for exponents over 79.3 million... for complete analysis...

Eric

trif · 2003-03-06, 01:54

None of those estimates takes into account the "clumping" seen in previous Mersenne primes. Are these just estimates given the average distance between primes, or is it a deeper analysis?

pakaran · 2003-03-06, 02:26

Well, there's a tight "clump" around 3M, but on the other hand some primes have been very isolated - M127 is slightly less than the fourth root of its successor. I think the "patterns" people may see are mostly just an artifact of the Poisson (sp?) distribution.

Pakaran

trif · 2003-03-07, 02:31

Below I have a table of all known Mersenne primes with Eric's predicted primes thrown in and M(n)/M(n-1) listed. Given the extreme variability in distance between one prime and the next, doing predictions with the kind of odds Eric believes he can requires being able to predict the outcome of that Poisson-like distribution, that there must be a pattern. However, the five predictions don't show as much variability in the ratio between one prime and the next as the actual series of known primes. The "missing" 11M Mersenne prime would be the closest of the batch (with the present M39), and it's very much on the edge of being a "clump". Only time will tell if hitting the 13M prime was lucky or if there truly is a pattern that allows close targeting of Mersenne primes.

1 2
2 3 1.50
3 5 1.67
4 7 1.40
5 13 1.86
6 17 1.31
7 19 1.12
8 31 1.63
9 61 1.96
10 89 1.45
11 107 1.20
12 127 1.18
13 521 4.10
14 607 1.16
15 1279 2.11
16 2203 1.72
17 2281 1.03
18 3217 1.41
19 4253 1.32
20 4423 1.03
21 9689 2.19
22 9941 1.02
23 11213 1.12
24 19937 1.77
25 21701 1.09
26 23209 1.07
27 44497 1.92
28 86243 1.93
29 110503 1.28
30 132049 1.19
31 216091 1.64
32 756839 3.50
33 859433 1.14
34 1257787 1.46
35 1398269 1.11
36 2976221 2.12
37 3021377 1.02
38 6972593 2.31
11000601 1.58
39? 13466917 1.22
18500000 1.37
31500000 1.70
42017086 1.33
56500000 1.34

Thomas11 · 2003-04-11, 11:36

My machine has just finished the range 41,564,021 - 41,976,829 up to 60 bit.
A total of 10613 exponents were tested and 340 factors were found.

-- Thomas.

2003-02-28, 08:28	#1
wackyeh Feb 2003 19 Posts	Complete testing of range at ~42 Million The following range is being worked on in every manner (except ECM)... 41,976,841 - 42,057,331 Currently... All exponents have been trial-factored thru 2^64... and are continuing on thru 2^69... Many of these esponents have also have P-1 done on them... higher than the standard Prime95 calculated limits... L-L tests are currently running on a number of these exponents as well... Due to the memory requirements (384MB)... the number of curves that would need to be tested (300 minimum)... and the time it would take for each curve... ECM is currently not feasible... (maybe when the P7 at 10GHz using SSE6 is around)... Eric

2003-04-11, 11:36	#10
Thomas11 Feb 2003 3600₈ Posts	range (41,564,021 - 41,976,829) done up to 2^60 My machine has just finished the range 41,564,021 - 41,976,829 up to 60 bit. A total of 10613 exponents were tested and 340 factors were found. -- Thomas.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Sequences from the 5 to 10 million range	Greebley	Aliquot Sequences	7	2015-09-04 08:22
500 - 600 Million Range	moo	LMH > 100M	32	2013-02-06 03:14
711 LL-tests in the 100 million digits range?	ET_	PrimeNet	9	2010-03-28 20:21
Range testing	Unregistered	Information & Answers	2	2009-12-11 05:13
GIMPS Credit for Exponents Between 79.3 Million and 596 Million	jinydu	Lounge	25	2006-12-22 10:54

2003-02-28, 22:52	#2
wackyeh Feb 2003 19₁₀ Posts	It has come to my attention that there has been interest in doing testing of exponents in the range that was predicted for the first 10 million digit Mersenne prime... of which I had made the "prediction"... a full 16 months before 2^13,466,917 was actually found... I have reserved the range listed above (41976841 - 42057331) thru George... and have been working on it... since before 2^13,466,917 was discovered... There are currently 15 machines tasked with this range... performing trial-factoring, P-1 and L-L testing... and an additional 6 preparing to start being tasked... Most are high-end machines... Anybody wishing to trial-factor, P-1 and/or L-L test the larger part of the predicted range (41,564,021 - 41,976,829 and 42,057,373 - 42,516373) is more than welcome to have at it... but as I have posted to the Mersenne mailing list... and the Yahoo list (now defunct)... there are NO guarantees or warranties offered up... Testing is at your own risk... of both success AND failure... Eric

2003-03-05, 18:13	#3
Thomas11 Feb 2003 2⁷×3×5 Posts	I would like to participate the search in that range. So I will start trial factoring in the lower range (41,564,021 - 41,976,829) up to 2^60 as a first step. Is that alright? Thomas.

2003-03-05, 18:29	#4
Thomas11 Feb 2003 2⁷×3×5 Posts	Eric, I've read your posting at http://www.mail-archive.com/mersenne@base.com/msg05046.html Now I have just a few questions: Is there some information available on the predictid ranges for M#41 and/or M#42? And what's known about M#44 and higher ones? Is there a prediction on how many Mersenne-Primes will or may be in the GIMPS range up to M79300000? Thomas. :?

2003-03-06, 01:54	#7
trif Aug 2002 2·101 Posts	None of those estimates takes into account the "clumping" seen in previous Mersenne primes. Are these just estimates given the average distance between primes, or is it a deeper analysis?

2003-03-06, 02:26	#8
pakaran Aug 2002 11111001₂ Posts	Well, there's a tight "clump" around 3M, but on the other hand some primes have been very isolated - M127 is slightly less than the fourth root of its successor. I think the "patterns" people may see are mostly just an artifact of the Poisson (sp?) distribution. Pakaran

2003-03-07, 02:31	#9
trif Aug 2002 2·101 Posts	Below I have a table of all known Mersenne primes with Eric's predicted primes thrown in and M(n)/M(n-1) listed. Given the extreme variability in distance between one prime and the next, doing predictions with the kind of odds Eric believes he can requires being able to predict the outcome of that Poisson-like distribution, that there must be a pattern. However, the five predictions don't show as much variability in the ratio between one prime and the next as the actual series of known primes. The "missing" 11M Mersenne prime would be the closest of the batch (with the present M39), and it's very much on the edge of being a "clump". Only time will tell if hitting the 13M prime was lucky or if there truly is a pattern that allows close targeting of Mersenne primes. 1 2 2 3 1.50 3 5 1.67 4 7 1.40 5 13 1.86 6 17 1.31 7 19 1.12 8 31 1.63 9 61 1.96 10 89 1.45 11 107 1.20 12 127 1.18 13 521 4.10 14 607 1.16 15 1279 2.11 16 2203 1.72 17 2281 1.03 18 3217 1.41 19 4253 1.32 20 4423 1.03 21 9689 2.19 22 9941 1.02 23 11213 1.12 24 19937 1.77 25 21701 1.09 26 23209 1.07 27 44497 1.92 28 86243 1.93 29 110503 1.28 30 132049 1.19 31 216091 1.64 32 756839 3.50 33 859433 1.14 34 1257787 1.46 35 1398269 1.11 36 2976221 2.12 37 3021377 1.02 38 6972593 2.31 11000601 1.58 39? 13466917 1.22 18500000 1.37 31500000 1.70 42017086 1.33 56500000 1.34