M2431321 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	24.5154	67.6471%	6000000	180000000	1.5164	9.0042%	26.0318	70.5602%	2.9131%
PrimeNet	2⁵⁹	0.0316	62.7119%	10000	180000	0.0019	2.5246%	0.0335	63.6533%	0.9414%
GPU72	2⁶³	0.6564	65.0794%	10000	150000	0.0017	1.3056%	0.6582	65.5353%	0.4559%
Difference	+5	+23.8590	+2.5677%	+5990000	+179850000	+1.5146	+7.6987%	+25.3736	+5.0249%	+5.0249%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2431321	44466390806979846634327	23	75.235	9144491987479203 3² × 1016054665275467	2020-10-13	9	1016054665275467	3,598.9	5,422,571	10,127,852

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.233%
2010-10-08T16:18:00	Oscar Östlin		40000	640000		-		-	-	0.007	-	-	1.453%
2011-01-18T22:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.526%
2011-02-27T04:32:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.070	-	-	3.936%
2017-10-23T01:37:45	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.088	-	-	4.026%
2019-03-20T05:14:07	Sid & Andy	Bullseye	6000000	180000000	12	-		-	-	1.516	-	-	9.004%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-11T08:38:00	Sturle Sunde	gerle.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T14:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-12-04T21:13:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.404	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.808	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.537	-	-
2015-10-25T20:34:59	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.074	-	-
2017-07-08T12:01:24	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.147	-	-
2019-07-17T09:51:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.29	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.224 GHz-days
Estimated T-Level:	4.050

Digits	B1	Curves	Complete	FacMiss
20	11000	81 / 100	0.810	44.305%
25	50000	81 / 280	0.289	74.841%

New Calculation Method

Total ECM effort:	7.224 GHz-days
Estimated T-Level:	4.050

Digits	B1	Complete	FacMiss
20	11000	3.115	4.436%
25	50000	0.288	74.957%
30	250000	0.018	98.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		79	7.045
50000	5000000	44466390806979846634327	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-04T18:46:00	paulie	iMac3.4	50000	5000000						3	0.268
2010-03-05T07:01:00	SubPrime	abd0	50000	5000000						3	0.268
2012-03-26T20:47:00	S36049	Wolle5	50000	5000000						3	0.268
2013-12-17T23:33:00	Bruce	apandya-DESK11	50000	5000000						3	0.268
2015-07-04T11:18:00	guru	w1	50000	5000000						3	0.268
2016-02-20T13:17:50	Sintax	cloud2	50000	5000000						3	0.268
2016-06-11T03:49:53	Jason U	Server7	50000	5000000						3	0.268
2016-10-12T13:14:13	Bruce	Desk6	50000	5000000						3	0.268
2017-04-20T23:14:54	Bruce	Desk6	50000	5000000						3	0.268
2017-11-21T07:41:25	Sebastian Hornbostel	V2	50000	5000000						3	0.268
2018-04-30T10:27:54	Bruce	Desk6	50000	5000000						3	0.268
2019-04-30T00:23:46	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.268
2020-04-22T17:38:36	mnd9	25836b	50000	5000000						3	0.268
2020-04-30T07:17:23	mnd9	libproj	50000	5000000						3	0.268
2020-05-10T18:18:42	mnd9	221Rb	50000	5000000						3	0.268
2020-05-26T03:15:00	mnd9	50871b	50000	5000000						3	0.268
2020-06-15T05:16:13	mnd9	50871b	50000	5000000						3	0.268
2020-06-28T00:07:58	GAN	LMS-02	50000	5000000						3	0.268
2020-07-05T01:33:34	GAN	LMS-02	50000	5000000						3	0.268
2020-07-11T21:47:29	debrouxl	8rd	50000	5000000						3	0.268
2020-07-23T17:43:16	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.268
2020-07-31T01:57:34	rextherunt	ice	50000	5000000						3	0.268
2020-08-07T06:33:20	GAN	LMS-17	50000	5000000						3	0.268
2020-08-16T07:23:26	mnd9	libproj	50000	5000000						3	0.268
2020-09-10T23:53:10	LordJulius	BlackboxNouveau	50000	5000000						7	0.624
2020-10-13T01:28:53	rextherunt	ice	50000	5000000	44466390806979846634327	75.235	2	2		2	0.178

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	EEDB6FF1E1BAC34C	0.164
2018-05-22T04:16:07	kkmrkkblmbrbk	old	EEDB6FF1E1BAC34C	0.164

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 = 6000000, B2 = 180000000 (P-1 stage 2)

B1 = 6000000 (P-1 stage 1)

B1 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 40000, B2 = 640000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 40000 (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