M2081851 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	57.3465	69.5652%	2500000	125000000	0.8746	7.2671%	58.2211	71.7770%	2.2117%
PrimeNet	2⁵⁸	0.0184	63.7931%	9000	160000	0.0016	2.6734%	0.0201	64.7611%	0.9680%
GPU72	2⁶²	0.2951	66.1290%	9000	140000	0.0015	1.3991%	0.2966	66.6029%	0.4739%
Difference	+7	+57.0514	+3.4362%	+2491000	+124860000	+0.8731	+5.8680%	+57.9245	+5.1740%	+5.1740%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.179%
2009-07-26T11:34:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.751%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.297%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.435%
2011-01-24T13:33:00	James Heinrich	Q6600	135000	2936250		-		-	-	0.027	-	-	2.431%
2016-07-07T00:37:27	Jocelyn Larouche	Manual testing	182413	5872500	12	-		-	-	0.047	-	-	2.999%
2016-11-04T12:39:35	Jocelyn Larouche	low 4M	218895	218895		-		-	-	0.021	-	-	1.075%
2016-11-07T03:11:22	Jocelyn Larouche	low 4M	262674	262674		-		-	-	0.025	-	-	1.181%
2016-11-11T16:54:52	Jocelyn Larouche	low 4M	315208	315208		-		-	-	0.030	-	-	1.294%
2017-04-02T14:54:12	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.267%
2017-05-13T16:00:17	Jocelyn Larouche	low 4M	390249	3902490	6	-		-	-	0.055	-	-	3.072%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T04:08:00	Sturle Sunde	kinner.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-17T18:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-02T08:36:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.472	-	-
2015-03-31T15:56:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.943	-	-
2015-03-31T15:56:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.795	-	-
2015-11-05T09:47:18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.589	-	-
2016-09-14T10:22:38	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.179	-	-
2019-04-01T03:15:22	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.36	-	-
2021-08-26T09:33:35	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	28.72	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.596 GHz-days
Estimated T-Level:	23.696

Digits	B1	Curves	Complete	FacMiss
20	11000	207 / 100	2.070	12.488%
25	50000	207 / 280	0.739	47.682%

New Calculation Method

Total ECM effort:	17.596 GHz-days
Estimated T-Level:	23.696

Digits	B1	Complete	FacMiss
20	11000	7.962	0.035%
25	50000	0.737	47.871%
30	250000	0.046	95.460%
35	1000000	0.002	99.783%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		207	17.60

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-05T13:31:00	SubPrime	dijkstra	50000	5000000						3	0.255
2009-10-31T22:15:00	JimBa	CIT3srvr	50000	5000000						3	0.255
2011-05-15T19:59:00	James Hintz	ryan	50000	5000000						3	0.255
2013-04-11T15:07:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-09-04T16:14:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.255
2015-07-25T10:02:00	guru	w1	50000	5000000						3	0.255
2016-02-20T15:42:53	Bruce	Desk8	50000	5000000						3	0.255
2016-05-17T13:01:59	Jason U	Server7	50000	5000000						3	0.255
2016-07-26T05:25:09	Bruce	test	50000	5000000						3	0.255
2017-01-11T06:34:32	Bruce	Desk6	50000	5000000						3	0.255
2017-07-29T07:09:57	Bruce	Desk6	50000	5000000						3	0.255
2017-12-22T21:34:12	Bruce	Desk6	50000	5000000						3	0.255
2018-05-16T03:31:23	Bruce	Desk6	50000	5000000						3	0.255
2018-10-14T01:18:44	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2020-01-02T14:24:19	TheJudger	myECM	50000	5000000						3	0.255
2020-01-09T19:58:57	mnd9	27016	50000	5000000						3	0.255
2020-01-17T03:22:50	EricP	Cannonfodder	50000	5000000						3	0.255
2020-01-22T12:29:02	EricP	Cannonfodder	50000	5000000						3	0.255
2020-02-03T04:07:34	mnd9	27016b	50000	5000000						3	0.255
2020-02-07T21:23:34	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-02-15T11:03:01	mnd9	eileen	50000	5000000						3	0.255
2020-02-23T08:19:44	mnd9	25836b	50000	5000000						3	0.255
2020-03-01T03:52:37	mnd9	colab2	50000	5000000						3	0.255
2020-03-07T05:10:33	mnd9	25836b	50000	5000000						3	0.255
2020-03-14T09:34:36	Alvin Bunk	BADCAT	50000	5000000						3	0.255
2020-03-22T11:23:11	kracker	O0	50000	5000000						3	0.255
2020-04-03T11:52:48	MarkS	laptop64	50000	5000000						3	0.255
2020-04-17T11:51:06	mnd9	221Rb	50000	5000000						3	0.255
2020-04-26T06:07:48	mnd9	221Rb	50000	5000000						3	0.255
2020-05-05T09:07:05	mnd9	libproj	50000	5000000						3	0.255
2020-06-04T12:38:09	mnd9	50871b	50000	5000000						3	0.255
2020-06-22T18:16:11	mnd9	touchdown	50000	5000000						3	0.255
2020-07-01T21:41:30	GAN	LMS-04	50000	5000000						3	0.255
2020-07-08T13:03:45	GAN	LMS-16	50000	5000000						3	0.255
2020-07-14T16:40:24	GAN	OSB-01	50000	5000000						3	0.255
2020-07-20T16:17:19	lycorn	colab_S	50000	5000000						3	0.255
2020-07-27T21:54:46	Nesowa	entropy_generator_2	50000	5000000						3	0.255
2020-08-03T12:49:16	GAN	LMS-11	50000	5000000						3	0.255
2020-08-09T07:43:01	daveward2005	Dave2	50000	5000000						3	0.255
2020-08-11T08:32:14	GAN	LMS-03	50000	5000000						3	0.255
2020-10-02T05:58:12	GAN	XPS	50000	5000000						7	0.595
2020-10-27T10:17:58	daveward2005	Dave2	50000	5000000						7	0.595
2020-10-29T17:37:19	rextherunt	ice	50000	5000000						7	0.595
2020-12-05T02:11:54	nokno	leo003	50000	5000000						7	0.595
2021-01-04T05:32:57	Zenzoma	AMD3970X	50000	5000000						7	0.595
2021-01-27T05:49:15	SXS2297	M-Laptop	50000	5000000						3	0.255
2021-02-20T04:41:17	Zenzoma	AMD3970X	50000	5000000						7	0.595
2021-03-24T11:03:11	daveward2005	MW	50000	5000000						7	0.595
2021-11-08T23:13:31	mnd9	50871b	50000	5000000						7	0.595
2021-11-08T23:15:34	RIHATEC	i7-3770K	50000	5000000						7	0.595
2021-11-09T04:53:52	RIHATEC	i7-3770K	50000	5000000						7	0.595
2021-11-09T21:22:42	RIHATEC	i7-3770K	50000	5000000						7	0.595
2022-02-23T18:11:22	C.D.B.	i7-6850K	50000	5000000						7	0.595

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2364C0F989737D51	0.137
2017-06-09T09:47:19	kkmrkkblmbrbk	c4.large	2364C0F989737D51	0.137

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 390249, B2 = 3902490 (P-1 stage 2)

B1 = 182413, B2 = 5872500 (P-1 stage 2)

B1 = 390249 (P-1 stage 1)

B1 = 315208 (P-1 stage 1)

B1 = 135000, B2 = 2936250 (P-1 stage 2)

B1 = 262674 (P-1 stage 1)

B1 = 218895 (P-1 stage 1)

B1 = 182413 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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