M2110351 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	28.2441	67.6471%	2500000	125000000	0.8746	7.9022%	29.1187	70.2037%	2.5566%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6802%	0.0198	63.0856%	1.0166%
GPU72	2⁶²	0.2911	64.5161%	10000	140000	0.0016	1.4528%	0.2927	65.0316%	0.5155%
Difference	+6	+27.9529	+3.1309%	+2490000	+124860000	+0.8730	+6.4494%	+28.8260	+5.1720%	+5.1720%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2110351	73093177138084154091717497	26	85.918	17317777265034146948 2² × 4329444316258536737	2020-07-10	4	4329444316258536737	5,792,925	2.249e+10	4.200e+10

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	-	-	0.224%
2009-08-02T06:49:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.878%
2010-12-30T22:20:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.511%
2011-01-25T16:15:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	2.768%
2016-07-19T03:39:19	Jocelyn Larouche	Manual testing	186340	6020000	12	-		-	-	0.048	-	-	3.383%
2016-11-08T17:01:23	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.241%
2017-05-31T03:38:56	Jocelyn Larouche	low 4M	372680	3726800	6	-		-	-	0.053	-	-	3.362%
2017-06-10T03:57:34	Jocelyn Larouche	low 4M	447216	4472160	6	-		-	-	0.064	-	-	3.584%
2017-07-21T10:39:10	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.902%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:05	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T15:11:00	Sturle Sunde	ghia.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-30T08:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-08-03T21:10:00	blahpy	Manual testing	2⁶²	2⁶³		-	-	0.465	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.930	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.770	-	-
2015-12-27T16:49:18	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.541	-	-
2016-10-05T13:07:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.082	-	-
2019-05-20T13:24:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.16	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.600 GHz-days
Estimated T-Level:	21.804

Digits	B1	Curves	Complete	FacMiss
20	11000	101 / 100	1.010	36.237%
25	50000	101 / 280	0.361	69.673%

New Calculation Method

Total ECM effort:	8.600 GHz-days
Estimated T-Level:	21.804

Digits	B1	Complete	FacMiss
20	11000	3.258	3.846%
25	50000	0.294	74.493%
30	250000	0.018	98.203%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		99	8.430
50000	5000000	73093177138084154091717497	2	0.170

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-26T22:06:00	Never Odd Or Even	Lap_Dir_2000	50000	5000000						3	0.255
2009-11-10T16:11:00	Samoflan	Parker	50000	5000000						3	0.255
2011-06-26T13:24:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-21T16:43:00	Jacques MOLNE	Old_faithfull	50000	5000000						3	0.255
2014-11-06T11:02:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.255
2015-08-03T18:31:00	guru	w1	50000	5000000						3	0.255
2016-02-22T04:04:05	Bruce	Desk6	50000	5000000						3	0.255
2016-05-30T01:24:43	Bruce	Desk6	50000	5000000						3	0.255
2016-08-19T00:36:17	Bruce	test	50000	5000000						3	0.255
2017-02-15T11:03:39	Bruce	Desk6	50000	5000000						3	0.255
2017-08-31T20:01:21	Bruce	Desk6	50000	5000000						3	0.255
2018-01-14T20:58:19	Bruce	Desk6	50000	5000000						3	0.255
2018-06-22T15:21:23	Bruce	Desk6	50000	5000000						3	0.255
2019-06-05T20:22:40	zar	eng1	50000	5000000						3	0.255
2020-01-19T12:21:33	volki	home	50000	5000000						3	0.255
2020-01-24T18:33:52	Bommer	2600X	50000	5000000						3	0.255
2020-02-02T18:12:19	David_McCann	i5	50000	5000000						3	0.255
2020-02-13T05:15:52	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.255
2020-02-18T03:49:35	mnd9	office2	50000	5000000						3	0.255
2020-02-25T02:29:09	Keysarecool	i9	50000	5000000						3	0.255
2020-03-03T04:02:51	mnd9	50869b	50000	5000000						3	0.255
2020-03-09T16:30:58	daveward2005	MW	50000	5000000						3	0.255
2020-03-14T08:31:55	daveward2005	Davy	50000	5000000						3	0.255
2020-03-17T04:17:45	IanGlencross	glenx24	50000	5000000						3	0.255
2020-03-27T10:53:10	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-04-08T11:52:06	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-04-21T23:44:04	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.255
2020-04-29T07:07:41	nordi	sweet16	50000	5000000						3	0.255
2020-05-11T14:27:35	nordi	sweet16	50000	5000000						3	0.255
2020-05-23T17:52:20	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-06-13T13:55:59	mnd9	kitchen	50000	5000000						3	0.255
2020-06-27T11:07:04	tonesforsins	tonesforsins	50000	5000000						3	0.255
2020-07-04T06:19:15	GAN	LMS-08	50000	5000000						3	0.255
2020-07-10T23:46:00	GAN	LMS-11	50000	5000000	73093177138084154091717497	85.918	2	2	3150514077535481	2	0.170

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	292F2F2F1DBC0D79	0.139
2018-04-02T23:38:25	kkmrkkblmbrbk	old	292F2F2F1DBC0D79	0.139

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 = 447216, B2 = 4472160 (P-1 stage 2)

B1 = 372680, B2 = 3726800 (P-1 stage 2)

B1 = 186340, B2 = 6020000 (P-1 stage 2)

B1 = 447216 (P-1 stage 1)

B1 = 372680 (P-1 stage 1)

B1 = 140000, B2 = 3010000 (P-1 stage 2)

B1 = 223608 (P-1 stage 1)

B1 = 186340 (P-1 stage 1)

B1 = 140000 (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)

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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