M1652741 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	36.0643	69.1176%	25000000	611144523990	2,273.8102	20.8322%	2,309.8745	75.5511%	6.4335%
Target	2⁶¹	0.1859	65.5738%	7000	70000	0.0007	1.1515%	0.1866	65.9702%	0.3964%
Difference	+7	+35.8784	+3.5439%	+24993000	+611144453990	+2,273.8095	+19.6807%	+2,309.6879	+9.5809%	+6.0370%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1652741	29453891029745804067011725741823707735606573599983 929	53	174.299	8910619095716087416906740300453521675691041004 2² × 3³ × 7 × 11 × 19 × 5039 × 1091581 × 5522851 × 7521233 × 11978503 × 20605566361	2022-12-01	11978503	20605566361	8.545e+10	77.383	143.09

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-02-29T17:08:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.761%
2012-02-29T17:12:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.124%
2012-02-29T18:08:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.379%
2012-02-29T18:12:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.580%
2012-02-29T19:09:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.746%
2012-02-29T19:12:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	1.890%
2012-02-29T20:08:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.016%
2012-02-29T20:11:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.129%
2012-02-29T21:09:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.232%
2012-02-29T21:13:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.326%
2012-03-01T06:08:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.293%
2012-03-01T07:09:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.188%
2017-12-24T12:25:08	Jocelyn Larouche	low 4M	2000000	20000000	12	-		-	-	0.203	-	-	5.503%
2018-02-02T15:34:05	Jocelyn Larouche	low 4M	1652741	20000000	12	-		-	-	0.181	-	-	5.425%
2018-02-08T12:52:27	Jocelyn Larouche	low 4M	1652741	40000000	12	-		-	-	0.255	-	-	6.173%
2018-02-17T20:09:12	Jocelyn Larouche	low 4M	1652741	80000000	12	-		-	-	0.404	-	-	6.931%
2018-03-30T19:42:34	Jocelyn Larouche	low 4M	1652741	165274100	12	-		-	-	0.721	-	-	7.734%
2018-07-28T01:07:14	mikr	Color	6000000	300000000	12	-		-	-	1.503	-	-	9.356%
2018-11-16T20:27:30	Jocelyn Larouche	Manual testing	1652741	330548200	12	-		-	-	1.336	-	-	8.509%
2018-11-19T17:38:28	Jocelyn Larouche	Manual testing	1652741	332200941	6	-		-	-	1.342	-	-	8.514%
2022-12-01T15:10:12	Naegi Makoto	5950X	25000000	611144523990			29453891029745804067011725741823707735606573599983 929	53	174.299	2,274	0.156	4,548	20.832%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-05-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.070	-	-
2010-04-28T16:30:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.093	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.186	-	-
2010-08-13T02:23:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.966	-	-
2016-02-23T16:28:44	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.594	-	-
2015-05-08T01:31:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.188	-	-
2015-05-08T17:30:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.261	-	-
2015-10-11T16:52:33	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.521	-	-
2017-10-20T14:50:27	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	9.043	-	-
2019-06-24T09:36:13	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	18.09	-	-

ECM factoring results:

Total ECM effort:	67.374 GHz-days
Estimated T-Level:	25.868

Digits	B1	Complete	FacMiss
20	11000	16.269	0.000%
25	50000	1.953	14.185%
30	250000	0.174	84.056%
35	1000000	0.013	98.737%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	16.59
250000	209979443		44	50.78

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-05-19T08:02:00	paulie	iMac3.4	50000	5000000						3	0.178
2009-06-08T18:16:00	James Hintz	08_060209	50000	5000000						3	0.178
2010-05-14T09:43:00	SubPrime	abd0	50000	5000000						3	0.178
2011-09-30T00:24:00	S36049	Wolle5	50000	5000000						3	0.178
2013-03-14T07:39:00	Donna Noble	opt4820	50000	5000000						3	0.178
2013-11-29T17:35:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-07-23T18:12:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-09-19T18:59:00	mikr	MSI	50000	5000000						12	0.711
2016-05-16T06:36:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-08-09T17:21:38	Bruce	DESK3	50000	5000000						3	0.178
2016-10-12T16:23:15	Bruce	DESK3	50000	5000000						3	0.178
2016-12-09T17:59:12	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-02-01T16:27:02	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-08-26T20:34:36	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2017-12-19T09:29:57	Bruce	DESK3	50000	5000000						3	0.178
2018-02-13T07:11:43	Lelikoid	QH	50000	5000000						3	0.178
2018-04-24T04:42:14	Lelikoid	QH	50000	5000000						3	0.178
2018-04-30T11:12:13	VictordeHollander	Manual testing	50000	5000000						220	13.04
2023-01-20T08:33:17	TJAOI	Manual testing	250000	209979443						44	50.78

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-25T00:00:00	ANONYMOUS	v4_computers	6EE64BF94A57FC89	0.078
1997-12-04T00:00:00	ANONYMOUS	v4_computers	6EE64BF94A57FC89	0.078
1997-12-21T00:00:00	ANONYMOUS	v4_computers	6EE64BF94A57FC89	0.078
1998-02-01T00:00:00	ANONYMOUS	v4_computers	6EE64BF94A57FC89	0.078
1998-12-06T00:00:00	ANONYMOUS	v4_computers	6EE64BF94A57FC89	0.078
2015-07-19T18:02:00	MadPoo	Manual testing	6EE64BF94A57FC89	0.078

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 = 25000000, B2 = 611144523990 (P-1 stage 2)

B1 = 25000000 (P-1 stage 1)

B1 = 6000000, B2 = 300000000 (P-1 stage 2)

B1 = 1652741, B2 = 332200941 (P-1 stage 2)

B1 = 1652741, B2 = 330548200 (P-1 stage 2)

B1 = 1652741, B2 = 165274100 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

B1 = 1652741, B2 = 80000000 (P-1 stage 2)

B1 = 1652741, B2 = 40000000 (P-1 stage 2)

B1 = 2000000, B2 = 20000000 (P-1 stage 2)

B1 = 1652741, B2 = 20000000 (P-1 stage 2)

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

B1 = 2000000 (P-1 stage 1)

B1 = 1652741 (P-1 stage 1)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10⁴

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10⁶

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10⁹

10¹⁰

10¹¹

10¹²

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