20180118, 19:14  #1 
"Luke Richards"
Jan 2018
Birmingham, UK
3^{2}·31 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). 
20180118, 19:42  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3·2,591 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. 
20180119, 01:03  #3 
Einyen
Dec 2003
Denmark
101011100111_{2} Posts 
As of midnight UTC Jan 19th (7pm EST Jan 18th):
Code:
Primes: 50 Factored: 29285461 LLD: 979577 LL: 658637 LLERR: 273 NOLL: 19923536 Total: 50847534 
20180119, 16:05  #4 
"Luke Richards"
Jan 2018
Birmingham, UK
427_{8} Posts 

20180119, 16:13  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5,309 Posts 
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.

20180120, 10:39  #6 
"Luke Richards"
Jan 2018
Birmingham, UK
3^{2}·31 Posts 
This occured to me just before I clicked "Submit" but I thought why let facts get into a nifty phrase ;)

20180120, 14:08  #7 
Einyen
Dec 2003
Denmark
2,791 Posts 
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 
20190101, 17:34  #8  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3,457 Posts 
Quote:
How about an annual update? Last fiddled with by kriesel on 20190101 at 17:34 

20190102, 15:05  #9 
Einyen
Dec 2003
Denmark
2,791 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 20190102 at 15:07 
20190102, 17:40  #10 
Einyen
Dec 2003
Denmark
2,791 Posts 
Here is an annual report from the archives:
Code:
20090101 20100101 20110101 20120101 20130101 20140101 20150101 20160101 20170101 20180101 20190101 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 LLD: 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 NOLL: 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: 20100101 20110101 20120101 20130101 20140101 20150101 20160101 20170101 20180101 20190101 Primes: +1 +0 +0 +0 +1 +0 +0 +1 +0 +2 Factored: +1304378 +488284 +238133 +126289 +197877 +301262 +288842 +381718 +204438 +267115 LLD: +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 NOLL: 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. Last fiddled with by ATH on 20190102 at 18:00 
20190104, 09:39  #11 
Romulan Interpreter
Jun 2011
Thailand
5·23·73 Posts 

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