M1400261 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	2⁶⁷	21.2203	68.6567%	500000	15000000	0.0714	4.9074%	21.2917	70.1948%	1.5381%
PrimeNet	2⁵⁶	0.0069	62.5000%	6500	110000	0.0007	2.7623%	0.0075	63.5358%	1.0358%
GPU72	2⁶⁰	0.1097	65.0000%	6000	70000	0.0005	1.2426%	0.1102	65.4349%	0.4349%
Difference	+7	+21.1106	+3.6567%	+494000	+14930000	+0.0709	+3.6647%	+21.1815	+4.7599%	+4.7599%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1400261	340574465508226404407	21	68.207	121611065904223 7 × 37 × 469540794997	2014-07-22	37	469540794997	72.905	1,416.3	2,645.2

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	-	-	0.246%
2003-02-16T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.500%
2003-09-21T00:00:00	ANONYMOUS	v4_computers	15000	202500		-		-	-	0.001	-	-	0.786%
2010-03-31T04:37:00	Rob_Dee	twopc	200000	400000		-		-	-	0.012	-	-	1.701%
2010-04-01T04:59:00	Rob_Dee	twopc	400000	600000		-		-	-	0.023	-	-	2.061%
2010-04-02T07:16:00	Rob_Dee	twopc	600000	800000		-		-	-	0.034	-	-	2.324%
2010-04-03T06:01:00	Rob_Dee	twopc	800000	1000000		-		-	-	0.045	-	-	2.537%
2010-04-04T06:06:00	Rob_Dee	twopc	1000000	1200000		-		-	-	0.056	-	-	2.717%
2010-04-05T05:33:00	Rob_Dee	twopc	1200000	1400000		-		-	-	0.067	-	-	2.874%
2010-04-06T05:14:00	Rob_Dee	twopc	1400000	1600000		-		-	-	0.078	-	-	3.014%
2010-04-07T06:30:00	Rob_Dee	twopc	1600000	1800000		-		-	-	0.089	-	-	3.140%
2010-04-08T05:51:00	Rob_Dee	twopc	1800000	2000000		-		-	-	0.100	-	-	3.255%
2010-04-09T04:50:00	Rob_Dee	twopc	2000000	2200000		-		-	-	0.111	-	-	3.361%
2010-04-10T03:58:00	Rob_Dee	twopc	2200000	2400000		-		-	-	0.122	-	-	3.459%
2010-04-11T05:58:00	Rob_Dee	twopc	2400000	2600000		-		-	-	0.133	-	-	3.550%
2010-04-12T04:51:00	Rob_Dee	twopc	2600000	2800000		-		-	-	0.145	-	-	3.636%
2010-04-13T06:06:00	Rob_Dee	twopc	2800000	3000000		-		-	-	0.156	-	-	3.717%
2010-04-14T05:36:00	Rob_Dee	twopc	3000000	3200000		-		-	-	0.167	-	-	3.793%
2010-04-15T05:39:00	Rob_Dee	twopc	3200000	3400000		-		-	-	0.178	-	-	3.866%
2010-04-16T04:59:00	Rob_Dee	twopc	3400000	3600000		-		-	-	0.189	-	-	3.935%
2010-04-17T04:40:00	Rob_Dee	twopc	3600000	3800000		-		-	-	0.200	-	-	4.001%
2010-04-18T05:51:00	Rob_Dee	twopc	3800000	4000000		-		-	-	0.211	-	-	4.064%
2010-04-19T05:27:00	Rob_Dee	twopc	4000000	4200000		-		-	-	0.222	-	-	4.124%
2010-04-20T04:55:00	Rob_Dee	twopc	4200000	4400000		-		-	-	0.233	-	-	4.182%
2010-04-21T04:28:00	Rob_Dee	twopc	4400000	4600000		-		-	-	0.244	-	-	4.238%
2010-04-22T05:43:00	Rob_Dee	twopc	4600000	4800000		-		-	-	0.255	-	-	4.291%
2010-04-23T05:38:00	Rob_Dee	twopc	4800000	5000000		-		-	-	0.266	-	-	4.343%
2010-04-24T06:16:00	Rob_Dee	twopc	5000000	5100000		-		-	-	0.277	-	-	4.367%
2016-03-17T19:13:49	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.907%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-27T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁷		-	-	0.014	-	-
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.055	-	-
2009-02-16T18:46:00	Sturle Sunde	gibus.ifi	2⁶⁰	2⁶¹		-	-	0.110	-	-
2011-01-08T22:47:00	BloodIce	Mjolnir4	2⁶¹	2⁶²		-	-	0.219	-	-
2011-04-05T20:59:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.140	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.367 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.367 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	11.76
50000	5000000	340574465508226404407	1	0.047
250000	35000000		50	13.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-12-31T17:42:00	Steve Scott	Abit	50000	5000000						1	0.047
2008-12-09T15:09:00	Matt	Dell	50000	5000000						3	0.141
2009-05-21T20:12:00	S00030	pc-1002	50000	5000000						3	0.141
2009-08-21T07:06:00	Lupo	yorick	50000	5000000						3	0.141
2009-12-26T06:38:00	sannerud.com	snap2	50000	5000000						3	0.141
2010-10-08T02:32:00	Charles A. Morris	magnetar	50000	5000000						3	0.141
2011-05-09T21:16:00	Bruce	GTLT-4540GZ	50000	5000000						3	0.141
2012-05-20T15:41:00	Oscar Östlin		50000	5000000						1	0.047
2012-07-20T15:16:00	soldake		50000	5000000						3	0.141
2013-05-20T09:58:00	OS1	Tina	50000	5000000						3	0.141
2013-12-03T05:43:00	OS1	Tina	50000	5000000						3	0.141
2014-03-13T08:23:00	Bruce	snowflake	50000	5000000						3	0.141
2014-07-22T17:07:00	Xyzzy	jv	50000	5000000	340574465508226404407	68.207	1	2		1	0.047
2018-12-21T12:15:35	TJAOI	Manual testing	50000	5000000						218	10.26
2021-09-21T09:29:16	TJAOI	Manual testing	250000	35000000						50	13.56

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 = 5100000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 4800000, B2 = 5000000 (P-1 stage 2)

B1 = 4800000 (P-1 stage 1)

B1 = 4600000, B2 = 4800000 (P-1 stage 2)

B1 = 4600000 (P-1 stage 1)

B1 = 4400000, B2 = 4600000 (P-1 stage 2)

B1 = 4400000 (P-1 stage 1)

B1 = 4200000, B2 = 4400000 (P-1 stage 2)

B1 = 4200000 (P-1 stage 1)

B1 = 4000000, B2 = 4200000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 3800000, B2 = 4000000 (P-1 stage 2)

B1 = 3800000 (P-1 stage 1)

B1 = 3600000, B2 = 3800000 (P-1 stage 2)

B1 = 3600000 (P-1 stage 1)

B1 = 3400000, B2 = 3600000 (P-1 stage 2)

B1 = 3400000 (P-1 stage 1)

B1 = 3200000, B2 = 3400000 (P-1 stage 2)

B1 = 3200000 (P-1 stage 1)

B1 = 3000000, B2 = 3200000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2800000, B2 = 3000000 (P-1 stage 2)

B1 = 2800000 (P-1 stage 1)

B1 = 2600000, B2 = 2800000 (P-1 stage 2)

B1 = 2600000 (P-1 stage 1)

B1 = 2400000, B2 = 2600000 (P-1 stage 2)

B1 = 2400000 (P-1 stage 1)

B1 = 2200000, B2 = 2400000 (P-1 stage 2)

B1 = 2200000 (P-1 stage 1)

B1 = 2000000, B2 = 2200000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1800000, B2 = 2000000 (P-1 stage 2)

B1 = 1800000 (P-1 stage 1)

B1 = 1600000, B2 = 1800000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 1400000, B2 = 1600000 (P-1 stage 2)

B1 = 1400000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1200000, B2 = 1400000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 1000000, B2 = 1200000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 800000, B2 = 1000000 (P-1 stage 2)

B1 = 800000 (P-1 stage 1)

B1 = 600000, B2 = 800000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000, B2 = 600000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 400000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

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

B1 = 15000, B2 = 202500 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

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

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