M2106353 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	28.2977	67.6471%	2500000	125000000	0.8746	7.9007%	29.1723	70.2032%	2.5561%
PrimeNet	2⁵⁸	0.0182	62.0690%	9000	160000	0.0016	2.6793%	0.0199	63.0852%	1.0163%
GPU72	2⁶²	0.2917	64.5161%	10000	140000	0.0016	1.4522%	0.2933	65.0314%	0.5153%
Difference	+6	+28.0060	+3.1309%	+2490000	+124860000	+0.8730	+6.4485%	+28.8790	+5.1717%	+5.1717%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2106353	7547337327625227242538991	25	82.642	1791565166813261415 3 × 5 × 23 × 59 × 61 × 1442884832593	2020-07-31	61	1442884832593	732,234	7,494.7	13,998

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%
2009-08-02T00:38:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.877%
2010-12-29T20:12:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.352%
2011-01-10T23:57:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.510%
2011-01-24T22:38:00	James Heinrich	Q6600	140000	3010000		-		-	-	0.028	-	-	2.767%
2016-07-17T03:53:37	Jocelyn Larouche	Manual testing	186340	6020000	12	-		-	-	0.048	-	-	3.382%
2016-11-08T17:01:21	Jocelyn Larouche	low 4M	223608	223608		-		-	-	0.021	-	-	1.241%
2017-05-31T03:38:55	Jocelyn Larouche	low 4M	372680	3726800	6	-		-	-	0.053	-	-	3.362%
2017-06-10T03:57:32	Jocelyn Larouche	low 4M	447216	4472160	6	-		-	-	0.064	-	-	3.583%
2017-07-09T14:53:34	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.901%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:05	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.073	-	-
2009-01-02T18:15:00	Sturle Sunde	fungo.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-03-29T23:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2013-09-04T10:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.466	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.932	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.774	-	-
2015-12-27T16:49:17	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.548	-	-
2016-10-01T21:16:26	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.095	-	-
2019-05-20T13:24:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.19	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.364 GHz-days
Estimated T-Level:	21.964

Digits	B1	Curves	Complete	FacMiss
20	11000	110 / 100	1.100	33.103%
25	50000	110 / 280	0.393	67.465%

New Calculation Method

Total ECM effort:	9.364 GHz-days
Estimated T-Level:	21.964

Digits	B1	Complete	FacMiss
20	11000	3.548	2.877%
25	50000	0.321	72.564%
30	250000	0.020	98.045%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		109	9.279
50000	5000000	7547337327625227242538991	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-12T21:19:00	S36049	Wolle3	50000	5000000						3	0.255
2009-11-14T07:33:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.255
2011-06-22T13:29:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-07T06:57:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-10-25T17:15:00	arnaud	srv-630	50000	5000000						3	0.255
2015-08-02T13:58:00	guru	w1	50000	5000000						3	0.255
2016-04-24T22:58:18	lettp	Home	50000	5000000						3	0.255
2016-05-28T13:06:25	Jason U	Server7	50000	5000000						3	0.255
2016-08-17T02:11:53	Bruce	test	50000	5000000						3	0.255
2017-02-11T05:53:36	Bruce	Desk6	50000	5000000						3	0.255
2017-08-29T00:05:38	Bruce	Desk6	50000	5000000						3	0.255
2017-12-09T13:46:38	Sid & Andy	Barrel_Of_Monkeys	50000	5000000						67	5.704
2020-07-17T22:11:37	mnd9	office2	50000	5000000						3	0.255
2020-07-18T20:48:31	mnd9	libproj	50000	5000000						3	0.255
2020-07-26T12:50:18	rextherunt	ice	50000	5000000						3	0.255
2020-07-31T14:03:00	daveward2005	MW	50000	5000000	7547337327625227242538991	82.642	1	2		1	0.085

date	userid	compid	res64	spent (GHz-days)
2015-11-14T22:44:56	MadPoo	Manual testing	B2B876B9032236__	0.138

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)

10⁰

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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