M2868001 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	41.6272	68.1159%	5000000	200000000	1.7498	8.5001%	43.3770	70.8261%	2.7102%
PrimeNet	2⁵⁹	0.0268	62.7119%	13000	240000	0.0028	2.9962%	0.0296	63.8291%	1.1172%
GPU72	2⁶³	0.5565	65.0794%	16000	280000	0.0034	1.8693%	0.5599	65.7321%	0.6528%
Difference	+6	+41.0707	+3.0366%	+4984000	+199720000	+1.7464	+6.6308%	+42.8171	+5.0940%	+5.0940%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2868001	81997680048302297978767	23	76.118	14295266990545383 3² × 8534297 × 186115271	2021-07-10	8534297	186115271	6,309.8	2.0393	2.1210

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.197%
2009-07-03T00:51:00	Carsten Kossendey	leela	15000	157500		-		-	-	0.003	-	-	0.611%
2010-12-21T22:27:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.228%
2011-01-03T14:36:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.319%
2011-01-21T23:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.465%
2011-02-11T00:26:00	markr	tiny	115000	2415000		-		-	-	0.027	-	-	2.361%
2016-08-29T10:01:39	Jocelyn Larouche	low4M	153065	4830000	6	-		-	-	0.046	-	-	2.915%
2016-12-18T19:43:10	Jocelyn Larouche	low 4M	183678	183678		-		-	-	0.021	-	-	1.035%
2017-01-10T10:25:07	Jocelyn Larouche	low 4M	220413	220413		-		-	-	0.025	-	-	1.139%
2017-03-11T20:25:01	Jocelyn Larouche	low 4M	317394	3173940	6	-		-	-	0.053	-	-	2.972%
2017-12-22T20:04:27	Jocelyn Larouche	low 4M	634788	6347880	6	-		-	-	0.106	-	-	3.790%
2019-10-26T17:52:04	masser	Manual testing	2870000	28700000	12	-		-	-	0.479	-	-	5.891%
2020-03-13T23:19:04	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	8.500%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:23	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-13T06:13:00	Sturle Sunde	letov.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2011-07-25T06:23:00	Rob_Dee	twopc	2⁶¹	2⁶²		-	-	0.107	-	-
2013-01-10T10:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.342	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.685	-	-
2015-04-21T09:21:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.303	-	-
2016-02-18T12:13:57	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.606	-	-
2017-11-12T17:07:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.211	-	-
2019-01-08T01:21:05	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.42	-	-
2021-06-07T10:35:50	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	20.84	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.204 GHz-days
Estimated T-Level:	4.400

Digits	B1	Curves	Complete	FacMiss
20	11000	88 / 100	0.880	41.295%
25	50000	88 / 280	0.314	72.990%

New Calculation Method

Total ECM effort:	9.204 GHz-days
Estimated T-Level:	4.400

Digits	B1	Complete	FacMiss
20	11000	2.839	5.850%
25	50000	0.257	77.371%
30	250000	0.016	98.433%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		87	9.100
50000	5000000	81997680048302297978767	1	0.105

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-24T12:31:00	willreid	jing	50000	5000000						3	0.314
2010-12-18T13:39:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.314
2013-04-22T10:11:00	Richard Kint	xps	50000	5000000						3	0.314
2015-07-12T18:47:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2015-07-12T19:15:00	Adel El-Atawy	MainMTV	50000	5000000						3	0.314
2019-05-30T10:24:22	Claude Portenier	Petit-Idiot	50000	5000000						3	0.314
2020-08-03T20:55:23	mnd9	f4b	50000	5000000						3	0.314
2020-08-11T02:17:53	Yuji HASEGAWA	lat5280	50000	5000000						3	0.314
2020-08-27T05:47:42	J.R. Allen	lapacer	50000	5000000						7	0.732
2020-09-30T07:45:52	mnd9	25836b	50000	5000000						7	0.732
2020-10-27T02:42:10	rextherunt	ice	50000	5000000						7	0.732
2020-11-30T09:17:38	Zenzoma	i7-6820HQ	50000	5000000						7	0.732
2021-01-04T17:32:09	Chun sung soo	home	50000	5000000						7	0.732
2021-02-02T21:30:34	Zenzoma	AMD3970X	50000	5000000						7	0.732
2021-03-04T22:05:11	mnd9	50869	50000	5000000						7	0.732
2021-04-08T19:49:33	Zenzoma	AMD3970X	50000	5000000						7	0.732
2021-06-02T13:02:33	daveward2005	Davy	50000	5000000						7	0.732
2021-07-10T11:10:37	MarkS	laptop64	50000	5000000	81997680048302297978767	76.118	1	2	7443388032225496	1	0.105

date	userid	compid	res64	spent (GHz-days)
1999-05-09T00:00:00	ANONYMOUS	v4_computers	AE34FE10F9C822AA	0.222
1999-07-12T00:00:00	ANONYMOUS	v4_computers	AE34FE10F9C822AA	0.222
2018-09-20T09:39:21	kkmrkkblmbrbk	old	AE34FE10F9C822AA	0.222

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 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 2870000, B2 = 28700000 (P-1 stage 2)

B1 = 2870000 (P-1 stage 1)

B1 = 634788, B2 = 6347880 (P-1 stage 2)

B1 = 634788 (P-1 stage 1)

B1 = 317394, B2 = 3173940 (P-1 stage 2)

B1 = 153065, B2 = 4830000 (P-1 stage 2)

B1 = 317394 (P-1 stage 1)

B1 = 115000, B2 = 2415000 (P-1 stage 2)

B1 = 220413 (P-1 stage 1)

B1 = 183678 (P-1 stage 1)

B1 = 153065 (P-1 stage 1)

B1 = 115000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 157500 (P-1 stage 2)

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)

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