M2280869 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	26.1325	67.6471%	518984	5189840	0.0737	3.8071%	26.2063	68.8788%	1.2317%
PrimeNet	2⁵⁸	0.0168	62.0690%	10000	190000	0.0019	2.9235%	0.0187	63.1779%	1.1089%
GPU72	2⁶²	0.2694	64.5161%	12000	200000	0.0021	1.7347%	0.2715	65.1317%	0.6155%
Difference	+6	+25.8632	+3.1309%	+506984	+4989840	+0.0716	+2.0724%	+25.9348	+3.7471%	+3.7471%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2280869	189831458543325220561921	24	77.329	41613845105379840 2⁹ × 3 × 5 × 19 × 59 × 211 × 22908073	2020-08-31	512	22908073	16,731	0.1190	0.2222

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.229%
2010-11-07T01:16:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.201%
2010-11-14T20:17:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.258%
2010-11-24T13:39:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.678%
2011-01-15T01:30:00	Oscar Östlin		85000	1742500		-		-	-	0.017	-	-	2.233%
2014-06-11T02:09:00	Jocelyn Larouche	Manual testing	113140	113140		-		-	-	0.011	-	-	0.869%
2014-10-06T21:12:00	Jocelyn Larouche	Manual testing	141280	141280		-		-	-	0.013	-	-	0.986%
2016-01-23T12:46:39	Jocelyn Larouche	Manual testing	518984	5189840	6	-		-	-	0.074	-	-	3.807%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15T16:43:00	Sturle Sunde	gowin.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-09T17:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.135	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.430	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.861	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.638	-	-
2015-11-01T21:51:01	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.276	-	-
2017-02-13T09:31:36	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	6.553	-	-
2019-09-10T14:32:17	Yxinity	Manual testing	2⁶⁷	2⁶⁸		-	-	13.11	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.602 GHz-days
Estimated T-Level:	21.786

Digits	B1	Curves	Complete	FacMiss
20	11000	100 / 100	1.000	36.603%
25	50000	100 / 280	0.357	69.923%

New Calculation Method

Total ECM effort:	8.602 GHz-days
Estimated T-Level:	21.786

Digits	B1	Complete	FacMiss
20	11000	3.226	3.972%
25	50000	0.292	74.711%
30	250000	0.018	98.221%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		93	8.000
50000	5000000	189831458543325220561921	7	0.602

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-29T18:10:00	oodaira	Win02	50000	5000000						3	0.258
2010-01-13T09:00:00	James Hintz	14_091909	50000	5000000						3	0.258
2011-11-10T03:48:00	S36049	Wolle5	50000	5000000						3	0.258
2013-08-30T15:30:00	arnaud	srv-630	50000	5000000						3	0.258
2015-04-08T02:22:00	Jason U	Server7	50000	5000000						3	0.258
2016-02-09T12:00:03	Tapio Pätilä	JULIUS	50000	5000000						3	0.258
2016-04-09T19:03:24	Bruce	Desk6	50000	5000000						3	0.258
2016-07-28T13:23:13	Bruce	Desk6	50000	5000000						3	0.258
2016-12-19T05:45:37	Bruce	Desk6	50000	5000000						3	0.258
2017-07-27T14:16:35	Bruce	Desk6	50000	5000000						3	0.258
2017-12-31T21:59:42	Bruce	Desk6	50000	5000000						3	0.258
2018-06-24T21:29:48	Bruce	Desk6	50000	5000000						3	0.258
2019-08-19T21:52:36	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-03-01T09:05:53	MarkS	desktop-i7	50000	5000000						3	0.258
2020-03-08T01:36:59	kracker	O0	50000	5000000						3	0.258
2020-03-15T04:16:21	MarkS	laptop64	50000	5000000						3	0.258
2020-03-23T23:04:05	Sergey Nosov	TS140-02	50000	5000000						3	0.258
2020-04-05T02:11:26	EricP	Cannonfodder	50000	5000000						3	0.258
2020-04-19T02:29:26	mnd9	colab2	50000	5000000						3	0.258
2020-04-27T04:32:14	mnd9	221Rb	50000	5000000						3	0.258
2020-05-06T09:25:09	EricP	Cannonfodder	50000	5000000						3	0.258
2020-05-18T22:52:10	Keysarecool	HPLaptop	50000	5000000						3	0.258
2020-06-07T17:54:30	GAN	KL-SCH05	50000	5000000						3	0.258
2020-06-23T15:34:34	Ahmed Azhad	c5.large.az	50000	5000000						3	0.258
2020-07-02T19:20:16	GAN	PG-MS	50000	5000000						3	0.258
2020-07-09T21:04:22	GAN	KA-HP	50000	5000000						3	0.258
2020-07-15T06:05:55	GAN	LMS-11	50000	5000000						3	0.258
2020-07-22T01:01:32	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.258
2020-07-30T18:58:11	mnd9	kitchen	50000	5000000						3	0.258
2020-08-04T11:58:21	daveward2005	Dave2	50000	5000000						3	0.258
2020-08-12T10:24:54	Yuji HASEGAWA	lat5280	50000	5000000						3	0.258
2020-08-31T08:32:18	daveward2005	Davy	50000	5000000	189831458543325220561921	77.329	7	2		7	0.602

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	77FA07462F28B290	0.150
2018-04-27T16:16:30	kkmrkkblmbrbk	old	77FA07462F28B290	0.150

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 = 518984, B2 = 5189840 (P-1 stage 2)

B1 = 518984 (P-1 stage 1)

B1 = 85000, B2 = 1742500 (P-1 stage 2)

B1 = 141280 (P-1 stage 1)

B1 = 113140 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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