M2373967 Mersenne number exponent details

is 2 ^2373967 - 1

has 714636 decimal digits

takes 0.160 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	25.1077	67.6471%	6000000	180000000	1.5164	8.9846%	26.6241	70.5538%	2.9068%
PrimeNet	2⁵⁹	0.0323	62.7119%	10000	170000	0.0018	2.4745%	0.0342	63.6346%	0.9227%
GPU72	2⁶³	0.6723	65.0794%	10000	140000	0.0017	1.2720%	0.6740	65.5235%	0.4442%
Difference	+5	+24.4354	+2.5677%	+5990000	+179860000	+1.5147	+7.7126%	+25.9501	+5.0303%	+5.0303%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2373967	3572901336131339686457	22	71.598	752517060290084 2² × 197 × 954970888693	2021-01-07	197	954970888693	255.63	5,096.6	9,519.0

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.231%
2010-02-12T10:19:00	Bud	annan	500000	10000000		-		-	-	0.100	-	-	4.387%
2018-02-09T00:35:36	Sid & Andy	Hand_In_The_Box	6000000	180000000	12	-		-	-	1.516	-	-	8.985%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:13	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-14T14:58:00	Sturle Sunde	gibsy.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-31T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.129	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.414	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.827	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.574	-	-
2015-10-31T16:44:13	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.148	-	-
2017-06-16T21:40:03	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.296	-	-
2019-04-01T13:34:44	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.59	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	9.777 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:	9.777 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	9.69
50000	5000000	3572901336131339686457	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-25T19:38:00	SubPrime	pitr	50000	5000000						3	0.267
2010-02-12T04:26:00	Dougal	dougal	50000	5000000						3	0.267
2012-01-16T16:24:00	Emiel	SlimLine	50000	5000000						3	0.267
2013-11-11T12:57:00	Bruce	apandya-DESK11	50000	5000000						3	0.267
2015-06-21T19:48:00	Jayder	HPJared	50000	5000000						3	0.267
2016-02-19T00:59:06	Sintax	cloud	50000	5000000						3	0.267
2016-05-19T22:52:37	Bruce	Desk6	50000	5000000						3	0.267
2016-09-08T16:05:12	Bruce	Desk6	50000	5000000						3	0.267
2017-03-14T13:20:28	Bruce	Desk6	50000	5000000						3	0.267
2017-10-22T21:10:05	Bruce	Desk6	50000	5000000						3	0.267
2018-03-13T21:07:44	Bruce	Desk6	50000	5000000						3	0.267
2018-09-24T20:56:59	Bruce	Desk6	50000	5000000						3	0.267
2020-03-24T02:21:47	mnd9	colab2	50000	5000000						3	0.267
2020-04-04T23:55:13	mnd9	221Rb	50000	5000000						3	0.267
2020-04-19T08:38:26	Sergey Nosov	TS140-02	50000	5000000						3	0.267
2020-04-27T02:07:26	mnd9	eileen	50000	5000000						3	0.267
2020-05-06T16:25:43	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.267
2020-05-19T02:52:22	mnd9	libproj	50000	5000000						3	0.267
2020-06-07T15:14:06	nordi	sweet16	50000	5000000						3	0.267
2020-06-24T05:44:50	LaurV	3tits	50000	5000000						3	0.267
2020-07-02T18:08:40	GAN	OSB-01	50000	5000000						3	0.267
2020-07-09T06:26:02	GAN	OSB-02	50000	5000000						3	0.267
2020-07-15T04:48:45	Ahmed Azhad	c5.large.az	50000	5000000						3	0.267
2020-07-22T12:43:23	Oliver Kruse	Krusen-NAS	50000	5000000						3	0.267
2020-07-27T20:56:29	GAN	LMS-15	50000	5000000						3	0.267
2020-08-04T06:26:28	GAN	LMS-18	50000	5000000						3	0.267
2020-08-12T05:42:42	GAN	LMS-06	50000	5000000						3	0.267
2020-08-30T23:30:26	M. R. Mayer	virga	50000	5000000						7	0.622
2020-10-18T13:26:26	GAN	AC-KL	50000	5000000						7	0.622
2020-10-29T18:09:33	lycorn	colab_S	50000	5000000						7	0.622
2020-12-05T09:10:41	daveward2005	Dave2	50000	5000000						7	0.622
2021-01-07T05:17:25	Chang Chia-Tche	ex-ctcpc	50000	5000000	3572901336131339686457	71.598	1	2	2574067571601136	1	0.089

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	EDBCF4B81B2E23DD	0.160
2018-05-14T04:50:21	kkmrkkblmbrbk	old	EDBCF4B81B2E23DD	0.160

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-07T05:47:21

mrh

3572901336131339686457

0E9F316BEB222BE9

2021-01-07T20:09:14

Lisander Viaene

3572901336131339686457

0E9F316BEB222BE9

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 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-01-07T20:09:14+00:00

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