M2793941 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	21.3336	67.6471%	3000000	90000000	0.8668	7.8350%	22.2004	70.1819%	2.5348%
PrimeNet	2⁵⁹	0.0275	62.7119%	12000	240000	0.0027	2.9260%	0.0302	63.8029%	1.0910%
GPU72	2⁶³	0.5712	65.0794%	15000	260000	0.0032	1.7890%	0.5744	65.7041%	0.6247%
Difference	+5	+20.7624	+2.5677%	+2985000	+89740000	+0.8636	+6.0460%	+21.6260	+4.4778%	+4.4778%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2793941	201973484454182730947757135961	30	97.350	36144908653078703334780 2² × 3² × 5 × 7 × 11² × 31 × 29587 × 258480979369	2020-12-11	29587	258480979369	1.149e+10	1,577.2	2,945.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.243%
2010-11-14T17:33:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.211%
2010-11-22T13:23:00	markr	tiny	100000	2075000		-		-	-	0.023	-	-	2.484%
2014-11-03T03:43:00	Jocelyn Larouche	Manual testing	122973	122973		-		-	-	0.014	-	-	0.946%
2016-05-07T02:42:11	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	3.184%
2017-07-30T01:18:50	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.576%
2019-12-14T11:06:45	BigBrother	Winston	3000000	90000000	12	-		-	-	0.867	-	-	7.835%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-02-12T21:03:00	Sturle Sunde	gaudi.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-08T01:28:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.351	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.703	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.337	-	-
2016-02-09T10:41:51	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.675	-	-
2017-10-19T22:32:33	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.349	-	-
2019-02-26T09:24:39	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.70	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.040 GHz-days
Estimated T-Level:	2.900

Digits	B1	Curves	Complete	FacMiss
20	11000	58 / 100	0.580	55.827%
25	50000	58 / 280	0.207	81.260%

New Calculation Method

Total ECM effort:	6.040 GHz-days
Estimated T-Level:	2.900

Digits	B1	Complete	FacMiss
20	11000	1.871	15.397%
25	50000	0.169	84.443%
30	250000	0.010	98.964%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		54	5.624
50000	5000000	201973484454182730947757135961	4	0.417

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-19T10:35:00	bayanne	MacBook	50000	5000000						3	0.312
2010-10-05T14:20:00	unconnected	X3220--xp	50000	5000000						3	0.312
2013-03-18T21:39:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-21T04:51:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-16T15:37:31	Sintax	cloud	50000	5000000						3	0.312
2016-05-27T20:06:47	lettp	Home	50000	5000000						3	0.312
2017-02-08T23:43:40	Bruce	eleven	50000	5000000						3	0.312
2017-08-14T14:58:58	JMGarcia	jmgarcia-pW07	50000	5000000						3	0.312
2018-01-21T09:21:03	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-11-22T19:42:41	Daniel Koszta	_	50000	5000000						3	0.312
2020-08-14T11:11:36	GAN	LMS-15	50000	5000000						3	0.312
2020-09-08T10:29:44	M. R. Mayer	virga	50000	5000000						7	0.729
2020-10-09T00:55:03	MarkS	desktop-i7	50000	5000000						7	0.729
2020-11-05T11:37:12	lycorn	colab_A_1	50000	5000000						7	0.729
2020-12-11T13:54:11	daveward2005	Dave2	50000	5000000	201973484454182730947757135961	97.350	4	2	8771848691887237	4	0.417

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	F6799F4A263FFC04	0.216
2018-08-30T01:06:29	kkmrkkblmbrbk	old	F6799F4A263FFC04	0.216

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 3000000, B2 = 90000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2075000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 122973 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront