How many exponents?

lukerichards · 2018-01-18, 19:14

I know that the milestones record lots of key information, but I wonder how many exponents have been checked overall by GIMPS? Is there a record of this?

(I know that I could in theory check how many primes there are up to a certain limit, but that would be an estimate).

Uncwilly · 2018-01-18, 19:42

Looking at: https://www.mersenne.org/primenet/
and then doing some sums.

From 2 to 999999999 there are 50847534 primes. Using these as exponents GIMPS has found factors for 29285332. Of the remaining, 979550 have been LL and DC'ed. Of the remaining, 658641 have had a single LL with no error. And there are 50 known primes.

GIMPS (either as an organization or its members) has verified all previous work done by others. So all of those exponents have been tested. A number of those with factors had their factors found after they were DC'ed (or LL'ed).

You could say all 50847534 have been checked in some form or other by GIMPS. And there are more above the 999999999 level that have also been tested (by factoring), but let's not count them.

ATH · 2018-01-19, 01:03

As of midnight UTC Jan 19th (7pm EST Jan 18th):

Code:

Primes:         50
Factored: 29285461
LL-D:       979577
LL:         658637
LLERR:         273
NO-LL:    19923536

Total:    50847534

lukerichards · 2018-01-19, 16:05

Quote:

Originally Posted by ATH

As of midnight UTC Jan 19th (7pm EST Jan 18th):

Code:

Primes:         50
Factored: 29285461
LL-D:       979577
LL:         658637
LLERR:         273
NO-LL:    19923536

Total:    50847534

Thanks (and to Uncwilly).

So Mersenne Primes seem to be one in a million then!

retina · 2018-01-19, 16:13

Quote:

Originally Posted by lukerichards

Thanks (and to Uncwilly).

So Mersenne Primes seem to be one in a million then!

More like 50 in 30 million since ~20 million are still to be tested in the range given. But this only covers the lower exponents up to 1 billion, it is expected that the frequency of primes will drop as the exponents get larger.

lukerichards · 2018-01-20, 10:39

Quote:

Originally Posted by retina

More like 50 in 30 million since ~20 million are still to be tested in the range given. But this only covers the lower exponents up to 1 billion, it is expected that the frequency of primes will drop as the exponents get larger.

This occured to me just before I clicked "Submit" but I thought why let facts get into a nifty phrase ;-)

ATH · 2018-01-20, 14:08

There are 39 Mersenne Primes in the first 1 million prime exponents, but then only 4 between prime number 1M and 2M, then 4 between prime number 2M and 3M and 1 between 3M and 4M and so far 2 between 4M and 5M:

Code:

		nth prime
M1:  p=2	1
M2:  p=3	2
M3:  p=5	3
M4:  p=7	4
M5:  p=13	6
M6:  p=17	7
M7:  p=19	8
M8:  p=31	11
M9:  p=61	18
M10: p=89	24
M11: p=107	28
M12: p=127	31
M13: p=521	98
M14: p=607	111
M15: p=1279	207
M16: p=2203	328
M17: p=2281	339
M18: p=3217	455
M19: p=4253	583
M20: p=4423	602
M21: p=9689	1196
M22: p=9941	1226
M23: p=11213	1357
M24: p=19937	2254
M25: p=21701	2435
M26: p=23209	2591
M27: p=44497	4624
M28: p=86243	8384
M29: p=110503	10489
M30: p=132049	12331
M31: p=216091	19292
M32: p=756839	60745
M33: p=859433	68301
M34: p=1257787	97017
M35: p=1398269	106991
M36: p=2976221	215208
M37: p=3021377	218239
M38: p=6972593	474908
M39: p=13466917	877615
M40: p=20996011 1329726
M41: p=24036583	1509263
M42: p=25964951	1622441
M43: p=30402457 1881339
M44: p=32582657 2007537
M45: p=37156667	2270720
M46: p=42643801 2584328
M47: p=43112609	2610944
M48: p=57885161	3443958
M49: p=74207281	4350601
M50: p=77232917 4517402

kriesel · 2019-01-01, 17:34

Quote:

Originally Posted by ATH

As of midnight UTC Jan 19th (7pm EST Jan 18th):

Code:

Primes:         50
Factored: 29285461
LL-D:       979577
LL:         658637
LLERR:         273
NO-LL:    19923536

Total:    50847534

Nice stats (both your posts). Are PRP lumped in with LL, or omitted?
How about an annual update?

ATH · 2019-01-02, 15:05

It is automated now from the hourly update:

http://hoegge.dk/mersenne/GIMPSstats.html

It is just an automated summation of this table: https://www.mersenne.org/primenet/

So yes LL and PRP are added together and LL DC + PRP DC.

ATH · 2019-01-02, 17:40

Here is an annual report from the archives:

Code:

	2009-01-01 2010-01-01 2011-01-01 2012-01-01 2013-01-01 2014-01-01 2015-01-01 2016-01-01 2017-01-01 2018-01-01 2019-01-01
	 00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC  00:00 UTC
	
Primes:         46         47         47         47         47         48         48         48         49         49         51
Factored: 25744917   27049295   27537579   27775712   27902001   28099878   28401140   28689982   29071700   29276138   29543253
LL-D:       495673     532623     577067     627964     674913     713928     758270     813831     910376     975815    1038378
LL:         429077     464289     483633     494289     517892     579833     625163     646299     642929     658914     682094
LLERR:        5642       2204       1713       1146        886        709        483        354        359        282        356
NO-LL:    24172179   22799076   22247495   21948376   21751796   21453139   21062431   20697020   20222121   19936336   19583402

Total:    50847534   50847534   50847534   50847534   50847535   50847535   50847535   50847534   50847534   50847534   50847534


Change per year:   2010-01-01 2011-01-01 2012-01-01 2013-01-01 2014-01-01 2015-01-01 2016-01-01 2017-01-01 2018-01-01 2019-01-01

Primes:                    +1         +0         +0         +0         +1         +0         +0         +1         +0         +2
Factored:            +1304378    +488284    +238133    +126289    +197877    +301262    +288842    +381718    +204438    +267115
LL-D:                  +36950     +44444     +50897     +46949     +39015     +44342     +55561     +96545     +65439     +62563
LL:                    +35212     +19344     +10656     +23603     +61941     +45330     +21136      -3370     +15985     +23180
LLERR:                  -3438       -491       -567       -260       -177       -226       -129         +5        -77        +74
NO-LL:               -1373103    -551581    -299119    -196580    -298657    -390708    -365411    -474899    -285785    -352934

In 2013, 2014 and 2015 there are 1 too many in one of the categories giving the wrong total.

In 2010+2011 the change in Factored is huge because the range 79.3M to 1000M opened up October? 2008 and was being factored. Then the change in Factored rose again from 2014 with the popularity of mfaktc and GPU factoring.

LaurV · 2019-01-04, 09:39

Quote:

Originally Posted by ATH

In 2010+2011 the change in Factored is huge because ~~the range ...~~ LaurV, Nucleon, Xyzzy, and few other kicked ass...

Fixed it for you

(see my posts about factoring 33xM ranges, at the time)

2018-01-18, 19:14	#1
lukerichards "Luke Richards" Jan 2018 Birmingham, UK 440₈ Posts	How many exponents? I know that the milestones record lots of key information, but I wonder how many exponents have been checked overall by GIMPS? Is there a record of this? (I know that I could in theory check how many primes there are up to a certain limit, but that would be an estimate).

2018-01-19, 01:03	#3
ATH Einyen Dec 2003 Denmark 2·1,667 Posts	As of midnight UTC Jan 19th (7pm EST Jan 18th): Code: Primes: 50 Factored: 29285461 LL-D: 979577 LL: 658637 LLERR: 273 NO-LL: 19923536 Total: 50847534

2019-01-02, 15:05	#9
ATH Einyen Dec 2003 Denmark 2×1,667 Posts	It is automated now from the hourly update: http://hoegge.dk/mersenne/GIMPSstats.html It is just an automated summation of this table: https://www.mersenne.org/primenet/ So yes LL and PRP are added together and LL DC + PRP DC. Last fiddled with by ATH on 2019-01-02 at 15:07

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Exponents which don't need any more ECM	MatWur-S530113	PrimeNet	8	2016-10-12 08:00
77.9M exponents	GP2	Data	9	2016-08-21 14:10
ECM for exponents above 20,000,000	TObject	Data	25	2014-05-24 15:45
Unreserving exponents(these exponents haven't been done)	jasong	Marin's Mersenne-aries	7	2006-12-22 21:59
>10,000,000 exponents	ninjabill	PrimeNet	5	2006-02-07 17:28

2018-01-18, 19:42	#2
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 10,607 Posts	Looking at: https://www.mersenne.org/primenet/ and then doing some sums. From 2 to 999999999 there are 50847534 primes. Using these as exponents GIMPS has found factors for 29285332. Of the remaining, 979550 have been LL and DC'ed. Of the remaining, 658641 have had a single LL with no error. And there are 50 known primes. GIMPS (either as an organization or its members) has verified all previous work done by others. So all of those exponents have been tested. A number of those with factors had their factors found after they were DC'ed (or LL'ed). You could say all 50847534 have been checked in some form or other by GIMPS. And there are more above the 999999999 level that have also been tested (by factoring), but let's not count them.