M2163923 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	27.5448	67.6471%	5000000	200000000	1.4896	8.9433%	29.0344	70.5405%	2.8934%
PrimeNet	2⁵⁸	0.0177	62.0690%	10000	180000	0.0018	2.8544%	0.0196	63.1517%	1.0827%
GPU72	2⁶²	0.2839	64.5161%	10000	160000	0.0017	1.5198%	0.2856	65.0554%	0.5393%
Difference	+6	+27.2609	+3.1309%	+4990000	+199840000	+1.4878	+7.4235%	+28.7487	+5.4851%	+5.4851%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2163923	19911663573259157027770679	26	84.042	4600825346664173593 97 × 47431189140867769	2021-03-06	97	47431189140867769	2,732,660	246,369,454	460,149,531

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-09T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.225%
2003-02-24T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.002	-	-	0.463%
2016-09-11T16:07:10	Jocelyn Larouche	low 4M	181500	14417920	12	-		-	-	0.091	-	-	4.000%
2017-05-13T16:00:11	Jocelyn Larouche	low 4M	363000	3630000	6	-		-	-	0.052	-	-	3.342%
2017-06-10T03:57:30	Jocelyn Larouche	low 4M	435600	4356000	6	-		-	-	0.062	-	-	3.563%
2017-06-28T04:14:44	Jocelyn Larouche	low 4M	522720	5227200	6	-		-	-	0.074	-	-	3.791%
2017-08-22T09:50:07	Jocelyn Larouche	low 4M	627264	6272640	12	-		-	-	0.089	-	-	4.025%
2017-08-24T01:00:12	Jocelyn Larouche	low 4M	752716	7527160	12	-		-	-	0.107	-	-	4.267%
2019-10-23T17:23:09	mikr	MSI	5000000	200000000	12	-		-	-	1.490	-	-	8.943%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.035	-	-
2016-02-23T16:29:07	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.035	-	-
2009-01-04T23:51:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.071	-	-
2009-01-08T02:19:00	Sturle Sunde	goscha.ifi	2⁶¹	2⁶²		-	-	0.142	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.454	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.907	-	-
2015-03-25T10:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.727	-	-
2015-12-30T18:01:38	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.453	-	-
2016-11-11T01:20:36	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.907	-	-
2019-05-13T13:38:17	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.81	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	13.412 GHz-days
Estimated T-Level:	22.786

Digits	B1	Curves	Complete	FacMiss
20	11000	156 / 100	1.560	20.849%
25	50000	156 / 280	0.557	57.227%

New Calculation Method

Total ECM effort:	13.412 GHz-days
Estimated T-Level:	22.786

Digits	B1	Complete	FacMiss
20	11000	5.048	0.642%
25	50000	0.457	63.346%
30	250000	0.028	97.227%
35	1000000	0.001	99.871%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		143	12.22
50000	5000000	19911663573259157027770679	6	0.513
50000	6750000		7	0.684

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-20T03:23:00	Nathan Slaven	q6600	50000	5000000						3	0.256
2009-12-08T08:54:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.256
2011-08-21T20:01:00	S36049	Wolle5	50000	5000000						3	0.256
2013-05-04T01:34:00	Xyzzy	J	50000	5000000						3	0.256
2015-01-29T05:42:00	arnaud	CHAMOT22	50000	5000000						3	0.256
2015-10-02T12:58:55	Wolfgang Fluck	C91F72025	50000	5000000						3	0.256
2016-03-02T07:37:57	Bruce	Desk6	50000	5000000						3	0.256
2016-06-19T18:09:13	Jason U	Server7	50000	5000000						3	0.256
2016-10-09T16:36:32	Bruce	Desk6	50000	5000000						3	0.256
2017-03-26T17:34:32	Bruce	Desk6	50000	5000000						3	0.256
2017-10-22T00:59:32	Bruce	Desk6	50000	5000000						3	0.256
2018-02-28T03:26:52	Bruce	Desk6	50000	5000000						3	0.256
2018-08-10T06:18:33	Bruce	Desk6	50000	5000000						3	0.256
2019-11-12T12:35:54	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-28T23:09:42	Nesowa	6700T	50000	5000000						3	0.256
2020-02-09T22:00:15	cappy95833	HomePC	50000	5000000						3	0.256
2020-02-14T04:43:39	EricP	Cannonfodder	50000	5000000						3	0.256
2020-02-21T17:49:36	mnd9	50869b	50000	5000000						3	0.256
2020-02-28T07:09:38	kracker	O0	50000	5000000						3	0.256
2020-03-08T18:02:45	IanGlencross	glenx24	50000	5000000						3	0.256
2020-03-13T02:05:48	mnd9	office2	50000	5000000						3	0.256
2020-03-20T12:24:06	IanGlencross	glenx24	50000	5000000						3	0.256
2020-04-01T17:15:15	EricP	Cannonfodder	50000	5000000						3	0.256
2020-04-15T10:32:41	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-04-25T05:06:50	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-05-03T09:20:37	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-05-14T22:25:40	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-06-01T00:26:28	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-06-21T13:43:31	daveward2005	MW	50000	5000000						3	0.256
2020-07-01T03:51:44	mnd9	25836b	50000	5000000						3	0.256
2020-07-07T21:22:42	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-07-13T16:20:37	lycorn	colab_A	50000	5000000						3	0.256
2020-07-19T20:18:35	GAN	OSB-02	50000	5000000						3	0.256
2020-07-26T03:54:11	GAN	LMS-12	50000	5000000						3	0.256
2020-08-02T11:57:23	GAN	LMS-14	50000	5000000						3	0.256
2020-08-10T04:37:11	lycorn	colab_S	50000	5000000						3	0.256
2020-08-24T09:45:59	daveward2005	Dave2	50000	5000000						7	0.598
2020-09-28T06:55:48	Brett Walker	brain	50000	5000000						7	0.598
2020-10-24T18:46:13	Keysarecool	Boat_Anchor	50000	5000000						7	0.598
2021-01-01T14:49:16	lycorn	colab_ES_1	50000	6750000						7	0.684
2021-01-28T14:58:00	mnd9	office2	50000	5000000						7	0.598
2021-02-05T04:27:25	mnd9	50871	50000	5000000						7	0.598
2021-03-06T13:41:31	mnd9	27016b	50000	5000000	19911663573259157027770679	84.042	6	2	3404102307612190	6	0.513

date	userid	compid	res64	spent (GHz-days)
1998-04-11T00:00:00	ANONYMOUS	v4_computers	E237391CC9A506A7	0.142
1999-02-21T00:00:00	Ethan O'Connor	v4_computers	E237391CC9A506A7	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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 752716, B2 = 7527160 (P-1 stage 2)

B1 = 181500, B2 = 14417920 (P-1 stage 2)

B1 = 627264, B2 = 6272640 (P-1 stage 2)

B1 = 522720, B2 = 5227200 (P-1 stage 2)

B1 = 752716 (P-1 stage 1)

B1 = 435600, B2 = 4356000 (P-1 stage 2)

B1 = 627264 (P-1 stage 1)

B1 = 363000, B2 = 3630000 (P-1 stage 2)

B1 = 522720 (P-1 stage 1)

B1 = 435600 (P-1 stage 1)

B1 = 363000 (P-1 stage 1)

B1 = 181500 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

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

B1 = 4096 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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