M3012367 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	2⁶⁹	39.6322	68.1159%	32739744	1866165408	16.3680	12.6559%	56.0002	72.1511%	4.0352%
PrimeNet	2⁶⁰	0.0510	63.3333%	12000	220000	0.0029	2.5170%	0.0539	64.2562%	0.9229%
GPU72	2⁶⁴	1.1816	65.6250%	13000	220000	0.0030	1.4274%	1.1846	66.1157%	0.4907%
Difference	+5	+38.4506	+2.4909%	+32726744	+1865945408	+16.3650	+11.2284%	+54.8156	+6.0355%	+6.0355%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3012367	1366723992465879985807151	25	80.177	226852171808063225 5² × 2173573 × 4174732973	2021-11-04	2173573	4174732973	160,551	28.324	52.427

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	-	-	0.120%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.200%
2010-10-18T15:08:00	markr	tiny	115000	2357500		-		-	-	0.029	-	-	2.365%
2010-12-26T11:01:00	Rob_Dee	twopc	150000	200000		-		-	-	0.019	-	-	1.087%
2010-12-27T10:06:00	Rob_Dee	twopc	200000	250000		-		-	-	0.025	-	-	1.222%
2010-12-28T09:22:00	Rob_Dee	twopc	250000	300000		-		-	-	0.031	-	-	1.339%
2010-12-29T08:52:00	Rob_Dee	twopc	300000	350000		-		-	-	0.037	-	-	1.443%
2010-12-30T10:02:00	Rob_Dee	twopc	350000	400000		-		-	-	0.044	-	-	1.536%
2010-12-31T09:16:00	Rob_Dee	twopc	400000	450000		-		-	-	0.050	-	-	1.621%
2011-01-01T08:24:00	Rob_Dee	twopc	450000	500000		-		-	-	0.056	-	-	1.700%
2011-01-02T08:12:00	Rob_Dee	twopc	500000	550000		-		-	-	0.062	-	-	1.772%
2011-01-03T07:51:00	Rob_Dee	twopc	550000	600000		-		-	-	0.068	-	-	1.840%
2011-01-04T09:08:00	Rob_Dee	twopc	600000	650000		-		-	-	0.074	-	-	1.904%
2011-01-05T09:11:00	Rob_Dee	twopc	650000	700000		-		-	-	0.081	-	-	1.964%
2011-01-06T08:39:00	Rob_Dee	twopc	700000	750000		-		-	-	0.087	-	-	2.021%
2011-01-07T09:09:00	Rob_Dee	twopc	750000	800000		-		-	-	0.093	-	-	2.075%
2011-01-08T08:31:00	Rob_Dee	twopc	800000	850000		-		-	-	0.099	-	-	2.126%
2011-01-09T09:45:00	Rob_Dee	twopc	850000	900000		-		-	-	0.105	-	-	2.175%
2011-01-10T17:35:00	Rob_Dee	twopc	950000	1000000		-		-	-	0.118	-	-	2.268%
2011-01-11T08:54:00	Rob_Dee	twopc	1000000	1100000		-		-	-	0.124	-	-	2.353%
2016-08-06T10:03:09	trebor		2000000	2000000		-		-	-	0.247	-	-	2.927%
2016-08-18T03:34:31	trebor		2250000	2250000		-		-	-	0.278	-	-	3.048%
2016-08-20T12:00:27	trebor		2500000	2500000		-		-	-	0.309	-	-	3.158%
2016-08-22T16:15:38	trebor		2750000	2750000		-		-	-	0.339	-	-	3.260%
2016-08-24T14:47:45	trebor		3000000	3000000		-		-	-	0.370	-	-	3.355%
2019-04-22T05:26:57	oodaira	com5	32739744	1866165408	12	-		-	-	16.37	-	-	12.656%
2022-01-26T04:01:32	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	6.838%

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	-	-
2009-01-27T06:32:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2010-09-08T16:49:00	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		-	-	1.240	-	-
2015-06-01T12:17:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.481	-	-
2017-02-06T12:13:40	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	4.961	-	-
2022-01-19T23:21:42	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.92	-	-
2018-07-16T08:59:43	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.92	-	-
2021-04-15T09:04:47	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	19.85	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.767 GHz-days
Estimated T-Level:	4.550

Digits	B1	Curves	Complete	FacMiss
20	11000	91 / 100	0.910	40.068%
25	50000	91 / 280	0.325	72.211%

New Calculation Method

Total ECM effort:	10.767 GHz-days
Estimated T-Level:	4.550

Digits	B1	Complete	FacMiss
20	11000	2.959	5.189%
25	50000	0.267	76.572%
30	250000	0.016	98.369%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4800000		7	0.799
50000	5000000		64	7.438
50000	5000000	1366723992465879985807151	6	0.697
50000	6125507		7	0.894
50000	6750000		7	0.939

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-06T13:21:00	Richard Kint	Desktop	50000	5000000						3	0.349
2011-05-24T20:52:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.349
2013-09-09T02:29:00	Bruce	fx6840-21	50000	5000000						3	0.349
2016-01-19T03:11:16	Bruce	Desk7	50000	5000000						3	0.349
2017-08-02T09:22:48	bayanne	iMac	50000	5000000						3	0.349
2020-09-16T19:39:24	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.814
2020-10-17T06:42:31	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.814
2020-11-19T18:50:57	IanGlencross	glenx24	50000	5000000						7	0.814
2020-12-29T21:35:16	lycorn	supernova	50000	6125507						7	0.894
2021-01-29T13:40:22	daveward2005	Davy	50000	5000000						7	0.814
2021-02-27T20:22:05	daveward2005	Davy	50000	5000000						7	0.814
2021-04-03T07:12:44	RIHATEC	i7-3770K	50000	5000000						7	0.814
2021-05-25T07:07:39	kutens	sol	50000	4800000						7	0.799
2021-07-13T22:43:36	Brett Walker	brain	50000	5000000						7	0.814
2021-08-18T21:28:11	J. W.	AMDNew	50000	6750000						7	0.939
2021-11-04T23:50:14	daveward2005	Dave2	50000	5000000	1366723992465879985807151	80.177	6	2	8582919582054875	6	0.697

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	EF01ADCC06386F__	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 = 32739744, B2 = 1866165408 (P-1 stage 2)

B1 = 32739744 (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 = 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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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