M3011429 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	19.7929	67.6471%	32745148	1866473436	16.3707	13.4730%	36.1636	72.0060%	4.3589%
PrimeNet	2⁶⁰	0.0510	63.3333%	12000	220000	0.0029	2.5169%	0.0539	64.2562%	0.9229%
GPU72	2⁶⁴	1.1819	65.6250%	13000	200000	0.0029	1.3880%	1.1848	66.1021%	0.4771%
Difference	+4	+18.6109	+2.0221%	+32732148	+1866273436	+16.3678	+12.0850%	+34.9788	+5.9039%	+5.9039%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3011429	58014271955494710548167	23	75.619	9632349285919527 3 × 3210783095306509	2021-03-31	3	3210783095306509	3,479.8	21,588,592	40,321,478

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.248%
2010-10-18T21:27:00	markr	tiny	115000	2357500		-		-	-	0.029	-	-	2.659%
2010-12-07T12:08:00	Rob_Dee	twopc	150000	200000		-		-	-	0.019	-	-	1.240%
2010-12-08T12:02:00	Rob_Dee	twopc	200000	250000		-		-	-	0.025	-	-	1.389%
2010-12-10T11:17:00	Rob_Dee	twopc	250000	300000		-		-	-	0.031	-	-	1.518%
2010-12-11T12:05:00	Rob_Dee	twopc	300000	350000		-		-	-	0.037	-	-	1.632%
2010-12-12T13:38:00	Rob_Dee	twopc	350000	400000		-		-	-	0.044	-	-	1.734%
2010-12-13T11:17:00	Rob_Dee	twopc	400000	450000		-		-	-	0.050	-	-	1.827%
2010-12-14T09:22:00	Rob_Dee	twopc	450000	500000		-		-	-	0.056	-	-	1.912%
2010-12-15T09:25:00	Rob_Dee	twopc	500000	550000		-		-	-	0.062	-	-	1.992%
2010-12-16T09:30:00	Rob_Dee	twopc	550000	600000		-		-	-	0.068	-	-	2.066%
2010-12-17T09:29:00	Rob_Dee	twopc	600000	650000		-		-	-	0.074	-	-	2.135%
2010-12-18T09:36:00	Rob_Dee	twopc	650000	700000		-		-	-	0.081	-	-	2.200%
2010-12-19T10:02:00	Rob_Dee	twopc	700000	750000		-		-	-	0.087	-	-	2.262%
2010-12-20T10:22:00	Rob_Dee	twopc	750000	800000		-		-	-	0.093	-	-	2.320%
2010-12-21T09:43:00	Rob_Dee	twopc	800000	850000		-		-	-	0.099	-	-	2.376%
2010-12-22T09:50:00	Rob_Dee	twopc	850000	900000		-		-	-	0.105	-	-	2.430%
2010-12-23T10:29:00	Rob_Dee	twopc	900000	950000		-		-	-	0.111	-	-	2.481%
2010-12-24T10:21:00	Rob_Dee	twopc	950000	1000000		-		-	-	0.118	-	-	2.529%
2010-12-25T10:14:00	Rob_Dee	twopc	1000000	1100000		-		-	-	0.124	-	-	2.622%
2016-08-05T03:46:53	trebor		2000000	2000000		-		-	-	0.247	-	-	3.240%
2016-08-17T21:31:42	trebor		2250000	2250000		-		-	-	0.278	-	-	3.370%
2016-08-20T08:30:38	trebor		2500000	2500000		-		-	-	0.309	-	-	3.489%
2016-08-22T12:55:25	trebor		2750000	2750000		-		-	-	0.339	-	-	3.598%
2016-08-24T10:47:56	trebor		3000000	3000000		-		-	-	0.370	-	-	3.699%
2019-04-05T17:45:35	oodaira	com5	32745148	1866473436	12	-		-	-	16.37	-	-	13.473%
2022-01-26T04:01:32	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	7.459%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-01-26T21:24:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-09-07T09:02:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.102	-	-
2013-01-07T13:52:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.326	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.652	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.241	-	-
2015-06-01T12:17:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.481	-	-
2017-02-06T12:13:40	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	4.963	-	-
2022-01-19T23:21:42	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.93	-	-
2018-07-16T08:59:42	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.93	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.205 GHz-days
Estimated T-Level:	3.100

Digits	B1	Curves	Complete	FacMiss
20	11000	62 / 100	0.620	53.627%
25	50000	62 / 280	0.221	80.106%

New Calculation Method

Total ECM effort:	7.205 GHz-days
Estimated T-Level:	3.100

Digits	B1	Complete	FacMiss
20	11000	2.000	13.534%
25	50000	0.181	83.464%
30	250000	0.011	98.893%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	6.624
50000	5000000	58014271955494710548167	5	0.581

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T06:09:00	James Hintz	07_060309	50000	5000000						3	0.349
2011-05-28T22:32:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.349
2013-09-11T22:01:00	arnaud	Chamot18	50000	5000000						3	0.349
2016-01-18T21:31:29	Bruce	Desk7	50000	5000000						3	0.349
2017-07-30T22:19:33	Bruce	desk	50000	5000000						3	0.349
2020-09-17T21:09:36	mnd9	75204b	50000	5000000						7	0.813
2020-10-16T23:20:46	mnd9	75204	50000	5000000						7	0.813
2020-11-19T10:05:05	daveward2005	Dave2	50000	5000000						7	0.813
2020-12-26T09:33:04	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.813
2021-01-27T04:30:15	daveward2005	Dave2	50000	5000000						7	0.813
2021-02-25T08:41:31	Zenzoma	AMD3970X	50000	5000000						7	0.813
2021-03-31T20:15:19	daveward2005	Dave2	50000	5000000	58014271955494710548167	75.619	5	2	334088534330161	5	0.581

date	userid	compid	res64	spent (GHz-days)
1999-08-31T00:00:00	ANONYMOUS	v4_computers	ACE3CD3558638D59	0.256

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 = 32745148, B2 = 1866473436 (P-1 stage 2)

B1 = 32745148 (P-1 stage 1)

B1 = 1000000, B2 = 119912100 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2750000 (P-1 stage 1)

B1 = 2500000 (P-1 stage 1)

B1 = 2250000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 1000000, B2 = 1100000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 950000, B2 = 1000000 (P-1 stage 2)

B1 = 950000 (P-1 stage 1)

B1 = 900000, B2 = 950000 (P-1 stage 2)

B1 = 900000 (P-1 stage 1)

B1 = 850000, B2 = 900000 (P-1 stage 2)

B1 = 850000 (P-1 stage 1)

B1 = 800000, B2 = 850000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 750000, B2 = 800000 (P-1 stage 2)

B1 = 750000 (P-1 stage 1)

B1 = 700000, B2 = 750000 (P-1 stage 2)

B1 = 700000 (P-1 stage 1)

B1 = 650000, B2 = 700000 (P-1 stage 2)

B1 = 650000 (P-1 stage 1)

B1 = 600000, B2 = 650000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 550000, B2 = 600000 (P-1 stage 2)

B1 = 550000 (P-1 stage 1)

B1 = 500000, B2 = 550000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 450000, B2 = 500000 (P-1 stage 2)

B1 = 450000 (P-1 stage 1)

B1 = 400000, B2 = 450000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 350000, B2 = 400000 (P-1 stage 2)

B1 = 350000 (P-1 stage 1)

B1 = 300000, B2 = 350000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 250000, B2 = 300000 (P-1 stage 2)

B1 = 250000 (P-1 stage 1)

B1 = 115000, B2 = 2357500 (P-1 stage 2)

B1 = 200000, B2 = 250000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 150000, B2 = 200000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

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10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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