M2042891 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	29.1767	69.1176%	4000000	200000000	1.3994	8.7579%	30.5762	71.8223%	2.7047%
PrimeNet	2⁵⁸	0.0188	63.7931%	9000	160000	0.0016	2.6639%	0.0204	64.7576%	0.9645%
GPU72	2⁶²	0.3007	66.1290%	9000	120000	0.0014	1.3293%	0.3022	66.5793%	0.4503%
Difference	+6	+28.8760	+2.9886%	+3991000	+199880000	+1.3980	+7.4286%	+30.2740	+5.2430%	+5.2430%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2042891	35669696170765397193089017	26	84.883	8730200527283491188 2² × 3 × 727516710606957599	2020-02-09	4	727516710606957599	2,784,554	3.779e+9	7.058e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-04-28T00:00:00	Jocelyn Larouche	v4_computers	1000	1000		-		-	-	9.53375e-5	-	-	0.005%
2002-05-05T00:00:00	Jocelyn Larouche	v4_computers	2000	2000		-		-	-	0.000	-	-	0.017%
2003-01-09T00:00:00	ANONYMOUS	v4_computers	25000	418750		-		-	-	0.004	-	-	1.085%
2010-12-28T23:08:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.349%
2011-01-04T22:09:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.507%
2011-01-31T07:11:00	markr	Manual testing	135000	3003750		-		-	-	0.028	-	-	2.735%
2014-10-19T12:31:00	Jocelyn Larouche	Manual testing	166418	166418		-		-	-	0.016	-	-	1.058%
2015-10-06T01:52:33	Bruno Victal	4790K-windows	500000	15000000	12	-		-	-	0.123	-	-	4.662%
2019-06-29T08:32:25	BigBrother	Winston	1000000	20000000	12	-		-	-	0.194	-	-	5.316%
2019-07-10T18:55:47	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.758%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.056	-	-
2009-01-03T01:05:00	Sturle Sunde	gluck.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-02-28T00:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-08-30T08:22:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.481	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.961	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.829	-	-
2015-11-01T21:51:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.658	-	-
2016-08-04T22:03:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.316	-	-
2019-03-22T01:11:12	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.427 GHz-days
Estimated T-Level:	3.200

Digits	B1	Curves	Complete	FacMiss
20	11000	64 / 100	0.640	52.560%
25	50000	64 / 280	0.229	79.534%

New Calculation Method

Total ECM effort:	5.427 GHz-days
Estimated T-Level:	3.200

Digits	B1	Complete	FacMiss
20	11000	2.065	12.688%
25	50000	0.187	82.978%
30	250000	0.011	98.858%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		63	5.343
50000	5000000	35669696170765397193089017	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-04T15:52:00	mognuts	hallowes	50000	5000000						3	0.254
2009-10-19T02:40:00	SubPrime	stor	50000	5000000						3	0.254
2011-03-11T15:43:00	Csaba Vágó	timigep	50000	5000000						3	0.254
2013-03-01T20:52:00	Donna Noble	opt4820	50000	5000000						3	0.254
2014-03-21T12:28:00	Bruce	snowflake	50000	5000000						3	0.254
2015-07-12T00:09:00	Syntony	Geomancer	50000	5000000						3	0.254
2016-02-19T05:04:57	Sintax	cloud	50000	5000000						3	0.254
2016-04-30T23:43:10	Bruce	Desk6	50000	5000000						3	0.254
2016-07-15T19:44:47	Bruce	test	50000	5000000						3	0.254
2016-11-23T10:34:32	NBCC		50000	5000000						3	0.254
2017-06-21T19:20:23	Bruce	Desk6	50000	5000000						3	0.254
2017-11-28T03:34:32	Lelikoid	QH	50000	5000000						3	0.254
2018-03-31T14:05:27	Bruce	Desk6	50000	5000000						3	0.254
2018-09-24T03:28:01	Clark B. Wierda	CF-27	50000	5000000						3	0.254
2019-12-23T21:13:34	Keysarecool	Boat_Anchor	50000	5000000						3	0.254
2019-12-29T18:14:48	daveward2005	Davy	50000	5000000						3	0.254
2020-01-03T06:32:21	TheJudger	myECM	50000	5000000						3	0.254
2020-01-10T17:41:51	mnd9	27016	50000	5000000						3	0.254
2020-01-18T11:46:21	daveward2005	MW	50000	5000000						3	0.254
2020-01-23T13:24:07	Alvin Bunk	BADCAT	50000	5000000						3	0.254
2020-02-06T08:18:39	Palantsevich	OfficeB01	50000	5000000						3	0.254
2020-02-09T08:14:22	mnd9	kitchen	50000	5000000	35669696170765397193089017	84.883	1	2	2328694032494168	1	0.085

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	34B12F05DDA5C097	0.134
2016-07-15T20:25:41	Mark Rose	raphael	34B12F05DDA5C097	0.134

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 135000, B2 = 3003750 (P-1 stage 2)

B1 = 166418 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 25000, B2 = 418750 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

B1 = 1000 (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