M2156521 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	27.6394	67.6471%	4000000	200000000	1.3994	8.8028%	29.0388	70.4950%	2.8479%
PrimeNet	2⁵⁸	0.0178	62.0690%	10000	170000	0.0018	2.8094%	0.0196	63.1346%	1.0656%
GPU72	2⁶²	0.2849	64.5161%	10000	160000	0.0017	1.5187%	0.2866	65.0550%	0.5389%
Difference	+6	+27.3545	+3.1309%	+3990000	+199840000	+1.3977	+7.2840%	+28.7522	+5.4400%	+5.4400%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2156521	34953754494601615567351	23	74.888	8104199888292675 3 × 5² × 571 × 189239927339	2020-08-16	571	189239927339	3,139.3	982.96	1,835.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.198%
2010-11-06T16:28:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.353%
2010-11-07T12:40:00	Jocelyn Larouche	Manual testing	45000	45000		-		-	-	0.004	-	-	0.477%
2010-11-10T11:27:00	Jocelyn Larouche	Manual testing	60000	60000		-		-	-	0.006	-	-	0.580%
2011-01-24T02:22:00	markr	tiny	120000	2340000		-		-	-	0.023	-	-	2.546%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	149763	149763		-		-	-	0.014	-	-	1.008%
2016-04-15T23:54:25	Jocelyn Larouche	Manual testing	240000	8843430	12	-		-	-	0.068	-	-	3.822%
2017-09-13T23:12:02	Jocelyn Larouche	low 4M	480000	4800000	6	-		-	-	0.068	-	-	3.682%
2017-09-19T22:20:06	Jocelyn Larouche	low 4M	576000	5760000	6	-		-	-	0.082	-	-	3.913%
2019-09-25T20:47:37	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.803%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-04T15:10:00	Sturle Sunde	jodel.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-06T18:08:00	Sturle Sunde	morovan.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-09-08T17:50:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.455	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.910	-	-
2015-03-22T08:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.733	-	-
2015-12-30T18:01:35	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.465	-	-
2016-11-04T03:09:03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.930	-	-
2019-05-20T13:24:29	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.86	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.392 GHz-days
Estimated T-Level:	21.964

Digits	B1	Curves	Complete	FacMiss
20	11000	110 / 100	1.100	33.103%
25	50000	110 / 280	0.393	67.465%

New Calculation Method

Total ECM effort:	9.392 GHz-days
Estimated T-Level:	21.964

Digits	B1	Complete	FacMiss
20	11000	3.548	2.877%
25	50000	0.321	72.564%
30	250000	0.020	98.045%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		108	9.222
50000	5000000	34953754494601615567351	2	0.171

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T05:33:00	dragon325	x-liberty	50000	5000000						3	0.256
2009-11-28T01:26:00	James Hintz	ryan	50000	5000000						3	0.256
2011-10-20T03:03:00	S36049	Wolle5	50000	5000000						3	0.256
2013-04-27T03:44:00	Donna Noble	opt4820	50000	5000000						3	0.256
2015-01-15T19:20:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-09-14T20:08:00	Syntony	Geomancer	50000	5000000						3	0.256
2016-02-29T22:32:49	Bruce	Desk6	50000	5000000						3	0.256
2016-06-17T18:55:19	lettp	Home	50000	5000000						3	0.256
2016-10-01T22:48:21	Bruce	Desk6	50000	5000000						3	0.256
2017-03-22T02:15:28	Bruce	Desk6	50000	5000000						3	0.256
2017-10-16T01:55:50	Bruce	Desk6	50000	5000000						3	0.256
2018-02-22T22:18:40	Bruce	Desk6	50000	5000000						3	0.256
2018-08-04T12:14:47	-Anonymous-	Kitchen	50000	5000000						3	0.256
2019-10-29T04:56:02	monsted	rootweiler	50000	5000000						3	0.256
2020-01-26T06:06:44	J.R. Allen	lapdell	50000	5000000						3	0.256
2020-02-08T09:54:56	Sebastian Hornbostel	NZXT	50000	5000000						3	0.256
2020-02-11T20:35:41	IanGlencross	glenx24	50000	5000000						3	0.256
2020-02-18T23:03:42	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-02-26T00:45:12	EricP	Cannonfodder	50000	5000000						3	0.256
2020-03-04T07:59:13	Nesowa	entropy_generator_2	50000	5000000						3	0.256
2020-03-10T09:59:36	MarkS	desktop-i7	50000	5000000						3	0.256
2020-03-18T02:55:08	Nesowa	entropy_generator_2	50000	5000000						3	0.256
2020-03-29T10:19:02	Brett Walker	brain	50000	5000000						3	0.256
2020-04-10T00:16:51	mnd9	221Rb	50000	5000000						3	0.256
2020-04-22T20:30:58	nordi	sweet16	50000	5000000						3	0.256
2020-04-30T07:53:16	nordi	sweet16	50000	5000000						3	0.256
2020-05-11T11:07:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-05-26T13:08:00	mnd9	50871b	50000	5000000						3	0.256
2020-06-14T05:47:10	mnd9	kitchen	50000	5000000						3	0.256
2020-06-28T06:33:22	GAN	LMS-16	50000	5000000						3	0.256
2020-07-05T07:24:25	GAN	LMS-18	50000	5000000						3	0.256
2020-07-11T21:14:00	GAN	LMS-08	50000	5000000						3	0.256
2020-07-17T20:07:44	daveward2005	Dave2	50000	5000000						3	0.256
2020-07-23T21:47:45	GAN	LMS-07	50000	5000000						3	0.256
2020-07-30T22:13:13	GAN	LMS-14	50000	5000000						3	0.256
2020-08-07T21:52:21	rextherunt	ice	50000	5000000						3	0.256
2020-08-16T00:30:01	GAN	LMS-17	50000	5000000	34953754494601615567351	74.888	2	2	7634542590932491	2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	64C838646AF32A70	0.142
2018-04-10T01:17:06	kkmrkkblmbrbk	old	64C838646AF32A70	0.142

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 576000, B2 = 5760000 (P-1 stage 2)

B1 = 480000, B2 = 4800000 (P-1 stage 2)

B1 = 240000, B2 = 8843430 (P-1 stage 2)

B1 = 576000 (P-1 stage 1)

B1 = 480000 (P-1 stage 1)

B1 = 120000, B2 = 2340000 (P-1 stage 2)

B1 = 240000 (P-1 stage 1)

B1 = 149763 (P-1 stage 1)

B1 = 120000 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 45000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

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