M2191619 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	27.1967	67.6471%	2500000	125000000	0.8746	7.9320%	28.0714	70.2133%	2.5663%
PrimeNet	2⁵⁸	0.0175	62.0690%	10000	180000	0.0018	2.8611%	0.0194	63.1542%	1.0852%
GPU72	2⁶²	0.2803	64.5161%	11000	160000	0.0018	1.5704%	0.2821	65.0734%	0.5572%
Difference	+6	+26.9164	+3.1309%	+2489000	+124840000	+0.8728	+6.3616%	+27.7892	+5.1399%	+5.1399%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2191619	16276252063631213496562448671	29	93.717	3713294159165259448965 3² × 5 × 82517647981450209977	2020-03-01	9	82517647981450209977	1.257e+9	4.286e+11	8.005e+11

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.226%
2010-11-04T10:39:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.199%
2010-11-09T10:50:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.355%
2011-01-11T23:58:00	markr	tiny	90000	1620000		-		-	-	0.017	-	-	2.206%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	119286	119286		-		-	-	0.011	-	-	0.890%
2014-10-12T23:56:00	Jocelyn Larouche	Manual testing	148572	148572		-		-	-	0.014	-	-	1.007%
2016-02-16T09:15:59	Jocelyn Larouche	Manual testing	442027	4420270	6	-		-	-	0.063	-	-	3.587%
2018-03-08T02:37:34	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.932%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	Dry Creek Photo	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:08	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.053	-	-
2009-01-02T23:53:00	Sturle Sunde	gigi.ifi	2⁶⁰	2⁶¹		-	-	0.070	-	-
2009-01-09T09:28:00	Sturle Sunde	gideon.ifi	2⁶¹	2⁶²		-	-	0.140	-	-
2013-01-23T08:20:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.448	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.896	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.705	-	-
2016-01-04T09:40:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.410	-	-
2016-12-01T14:35:15	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.819	-	-
2019-04-08T13:40:40	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.64	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.535 GHz-days
Estimated T-Level:	2.650

Digits	B1	Curves	Complete	FacMiss
20	11000	53 / 100	0.530	58.704%
25	50000	53 / 280	0.189	82.727%

New Calculation Method

Total ECM effort:	4.535 GHz-days
Estimated T-Level:	2.650

Digits	B1	Complete	FacMiss
20	11000	1.710	18.092%
25	50000	0.155	85.683%
30	250000	0.010	99.053%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		51	4.364
50000	5000000	16276252063631213496562448671	2	0.171

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-22T15:59:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.257
2009-12-13T16:04:00	SubPrime	stor	50000	5000000						3	0.257
2011-09-09T08:21:00	Lukasz Wrobel	WORK_lupo	50000	5000000						3	0.257
2013-05-22T18:21:00	hiems	Laptop	50000	5000000						3	0.257
2015-03-10T12:46:00	Lukasz Wrobel	i-1	50000	5000000						3	0.257
2015-12-15T17:24:22	guru	w1	50000	5000000						3	0.257
2016-03-08T21:33:09	Jason U	Server7	50000	5000000						3	0.257
2016-06-27T06:07:07	Jason U	Server7	50000	5000000						3	0.257
2016-11-08T03:21:43	Bruce	Desk6	50000	5000000						3	0.257
2017-04-18T20:15:13	Bruce	Desk6	50000	5000000						3	0.257
2017-11-05T14:34:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.257
2018-03-21T21:49:45	Bruce	Desk6	50000	5000000						3	0.257
2018-09-16T05:24:52	Bruce	Desk6	50000	5000000						3	0.257
2020-01-30T17:42:30	EricP	Cannonfodder	50000	5000000						3	0.257
2020-02-14T15:38:53	S04803	lfmcal	50000	5000000						3	0.257
2020-02-16T12:53:31	mnd9	eileen	50000	5000000						3	0.257
2020-02-24T08:02:54	Brett Walker	brain	50000	5000000						3	0.257
2020-03-02T01:07:31	mnd9	27016b	50000	5000000	16276252063631213496562448671	93.717	2	2	8185608410851241	2	0.171

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	Dry Creek Photo	v4_computers	30B98FC9AFDE35C0	0.144
2018-04-15T04:53:51	kkmrkkblmbrbk	old	30B98FC9AFDE35C0	0.144

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 = 442027, B2 = 4420270 (P-1 stage 2)

B1 = 442027 (P-1 stage 1)

B1 = 90000, B2 = 1620000 (P-1 stage 2)

B1 = 148572 (P-1 stage 1)

B1 = 119286 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000 (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