M2127751 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	56.1094	68.1159%	2500000	125000000	0.8746	7.2833%	56.9840	70.4381%	2.3222%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	160000	0.0016	2.6844%	0.0197	63.0872%	1.0182%
GPU72	2⁶²	0.2887	64.5161%	10000	140000	0.0016	1.4552%	0.2904	65.0325%	0.5164%
Difference	+7	+55.8206	+3.5998%	+2490000	+124860000	+0.8730	+5.8281%	+56.6937	+5.4057%	+5.4057%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.180%
2009-08-03T23:22:00	harlee	P4_2600	20000	265000		-		-	-	0.003	-	-	0.759%
2011-01-01T00:57:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.298%
2011-01-12T23:59:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.437%
2011-01-25T16:23:00	James Heinrich	i7-920	140000	3045000		-		-	-	0.028	-	-	2.477%
2016-06-28T05:38:31	Jocelyn Larouche	Manual testing	210000	6090000	12	-		-	-	0.051	-	-	3.108%
2017-08-19T15:19:15	Jocelyn Larouche	low 4M	420000	4200000	6	-		-	-	0.060	-	-	3.164%
2017-08-30T00:32:09	Jocelyn Larouche	low 4M	504000	5040000	6	-		-	-	0.072	-	-	3.374%
2017-09-14T19:10:21	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.283%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-04T17:17:00	Sturle Sunde	buxtehude.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-04T03:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-09-06T08:32:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.461	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.923	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.756	-	-
2015-12-27T16:49:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.512	-	-
2016-10-15T17:13:27	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.024	-	-
2019-04-29T13:20:35	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.05	-	-
2021-08-12T13:16:27	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	28.10	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.208 GHz-days
Estimated T-Level:	23.554

Digits	B1	Curves	Complete	FacMiss
20	11000	199 / 100	1.990	13.533%
25	50000	199 / 280	0.711	49.067%

New Calculation Method

Total ECM effort:	17.208 GHz-days
Estimated T-Level:	23.554

Digits	B1	Complete	FacMiss
20	11000	7.704	0.045%
25	50000	0.714	48.969%
30	250000	0.045	95.585%
35	1000000	0.002	99.789%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	191	16.28
50000	6750000	7	0.682
76620	24176890	1	0.246

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-17T00:45:00	maxybo	CB418E216	50000	5000000						3	0.256
2009-11-19T20:28:00	SubPrime	abd0	50000	5000000						3	0.256
2011-07-21T14:50:00	Beat Bucheli	I7	50000	5000000						3	0.256
2013-04-22T08:27:00	hiems	Laptop	50000	5000000						3	0.256
2014-12-03T07:20:00	AdolfNor	PC4	50000	5000000						3	0.256
2015-08-10T08:00:00	guru	w6	50000	5000000						3	0.256
2016-02-25T02:21:34	arnaud	PORTABLE08	50000	5000000						3	0.256
2016-06-08T14:51:35	lettp	Home	50000	5000000						3	0.256
2016-08-30T18:15:43	Bruce	test	50000	5000000						3	0.256
2017-03-04T06:09:43	Bruce	Desk6	50000	5000000						3	0.256
2017-09-14T17:49:05	Bruce	Desk6	50000	5000000						3	0.256
2018-01-29T19:43:36	Bruce	Desk6	50000	5000000						3	0.256
2018-07-14T14:51:25	Bruce	Desk6	50000	5000000						3	0.256
2019-08-27T14:40:21	prime235711	prime235711	50000	5000000						3	0.256
2020-01-18T06:15:39	mnd9	221Rb	50000	5000000						3	0.256
2020-01-24T12:43:04	Yxinity	Olga	50000	5000000						3	0.256
2020-02-02T23:41:03	Nesowa	6700T	50000	5000000						3	0.256
2020-02-09T23:17:42	mnd9	kitchen	50000	5000000						3	0.256
2020-02-17T05:25:44	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-02-24T07:08:52	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-03-02T11:13:09	Alvin Bunk	BADCAT	50000	5000000						3	0.256
2020-03-08T06:35:08	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-03-17T04:25:08	Corey	Computer	50000	5000000						3	0.256
2020-03-25T05:18:23	Brett Walker	brain	50000	5000000						3	0.256
2020-04-06T03:50:03	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-04-20T00:27:45	daveward2005	Davy	50000	5000000						3	0.256
2020-04-27T16:16:13	EricP	Cannonfodder	50000	5000000						3	0.256
2020-05-07T19:12:56	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-05-21T01:49:07	mnd9	75203	50000	5000000						3	0.256
2020-06-25T07:39:39	nordi	sweet16	50000	5000000						3	0.256
2020-07-05T07:18:11	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.256
2020-07-10T08:10:57	mnd9	25836b	50000	5000000						3	0.256
2020-07-15T21:41:39	GAN	XPS	50000	5000000						3	0.256
2020-07-21T22:55:47	GAN	LMS-13	50000	5000000						3	0.256
2020-07-28T10:52:38	GAN	LMS-02	50000	5000000						3	0.256
2020-08-07T18:40:10	mnd9	libproj	50000	5000000						3	0.256
2020-08-07T23:53:07	nokno	leo003	50000	5000000						3	0.256
2020-08-13T22:19:36	GAN	KA-AC	50000	5000000						3	0.256
2020-09-02T07:16:48	mnd9	25836b	50000	5000000						7	0.597
2020-10-05T00:09:23	mnd9	75204	50000	5000000						7	0.597
2020-11-01T01:23:12	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.597
2020-11-09T21:38:35	Bruno Victal	Manual testing	76620	24176890						1	0.246
2021-01-21T12:57:28	C.D.B.	i7-6850K	50000	5000000						7	0.597
2021-02-19T00:15:48	Zenzoma	AM3700X_1	50000	5000000						7	0.597
2021-02-19T15:50:03	-Anonymous-		50000	5000000						7	0.597
2021-03-22T02:23:39	C.D.B.	i7-6850K	50000	5000000						7	0.597
2021-05-07T20:46:30	Zenzoma	AMD3970X	50000	5000000						7	0.597
2021-06-19T23:35:58	LaurV	butu	50000	6750000						7	0.682
2021-08-04T18:09:58	RIHATEC	i7-3770K	50000	5000000						7	0.597
2021-10-11T12:52:26	mnd9	office2	50000	5000000						7	0.597
2021-12-27T09:25:30	daveward2005	d12436	50000	5000000						7	0.597

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2D35F288433BA5D2	0.140
2018-04-05T09:54:31	kkmrkkblmbrbk	old	2D35F288433BA5D2	0.140

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 = 504000, B2 = 5040000 (P-1 stage 2)

B1 = 420000, B2 = 4200000 (P-1 stage 2)

B1 = 210000, B2 = 6090000 (P-1 stage 2)

B1 = 504000 (P-1 stage 1)

B1 = 420000 (P-1 stage 1)

B1 = 140000, B2 = 3045000 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (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