M2371709 Mersenne number exponent details

is 2 ^2371709 - 1

has 713956 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	25.1316	67.6471%	3000000	100000000	0.8115	7.8376%	25.9432	70.1828%	2.5357%
PrimeNet	2⁵⁹	0.0324	62.7119%	10000	170000	0.0018	2.4741%	0.0342	63.6344%	0.9225%
GPU72	2⁶³	0.6729	65.0794%	10000	140000	0.0017	1.2717%	0.6746	65.5235%	0.4441%
Difference	+5	+24.4587	+2.5677%	+2990000	+99860000	+0.8099	+6.5659%	+25.2685	+4.6593%	+4.6593%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2371709	28625412758162949323033	23	74.600	6034764964454524 2² × 1508691241113631	2020-07-01	4	1508691241113631	2,201.1	8,051,718	15,038,366

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%
2010-10-11T15:24:00	Oscar Östlin		40000	630000		-		-	-	0.007	-	-	1.440%
2011-01-18T00:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.523%
2011-01-27T00:59:00	James Heinrich	i7-920	160000	3640000		-		-	-	0.034	-	-	3.008%
2016-01-11T11:25:32	mikr	MSI	3000000	100000000	12	-		-	-	0.812	-	-	7.838%

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	-	-
2009-01-15T21:38:00	Sturle Sunde	jodel.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-31T12:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.130	-	-
2013-01-23T08:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.414	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.828	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.575	-	-
2015-10-30T09:42:39	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.151	-	-
2017-06-16T21:40:02	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.302	-	-
2019-04-08T13:40:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.60	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.510 GHz-days
Estimated T-Level:	3.100

Digits	B1	Curves	Complete	FacMiss
20	11000	62 / 100	0.620	53.627%
25	50000	62 / 280	0.221	80.106%

New Calculation Method

Total ECM effort:	5.510 GHz-days
Estimated T-Level:	3.100

Digits	B1	Complete	FacMiss
20	11000	2.000	13.534%
25	50000	0.181	83.464%
30	250000	0.011	98.893%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	5.332
50000	5000000	28625412758162949323033	2	0.178

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-26T16:51:00	S36049	Wolle3	50000	5000000						3	0.267
2010-08-10T20:10:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.267
2012-01-19T16:13:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-12T17:05:00	Kripke	Kripke	50000	5000000						3	0.267
2015-06-24T19:42:00	nranks	wlaptop	50000	5000000						3	0.267
2016-02-18T07:47:52	Sintax	cloud2	50000	5000000						3	0.267
2016-05-16T16:18:01	lettp	Home	50000	5000000						3	0.267
2016-09-07T17:25:02	Bruce	Desk6	50000	5000000						3	0.267
2017-03-12T21:14:32	Bruce	Desk6	50000	5000000						3	0.267
2017-10-21T02:46:25	Bruce	Desk6	50000	5000000						3	0.267
2018-03-12T03:01:30	Bruce	Desk6	50000	5000000						3	0.267
2018-09-21T13:58:52	Bruce	Desk6	50000	5000000						3	0.267
2020-03-22T02:18:21	IanGlencross	glenx24	50000	5000000						3	0.267
2020-04-03T06:44:20	mat10243x	N1	50000	5000000						3	0.267
2020-04-17T23:55:53	nranks	wlaptop	50000	5000000						3	0.267
2020-04-26T13:40:17	nordi	sweet16	50000	5000000						3	0.267
2020-05-05T00:19:33	Keysarecool	Boat_Anchor	50000	5000000						3	0.267
2020-05-17T09:50:28	mnd9	50871b	50000	5000000						3	0.267
2020-06-04T09:01:15	daveward2005	MW	50000	5000000						3	0.267
2020-06-23T04:03:34	LaurV	3tits	50000	5000000						3	0.267
2020-07-01T21:52:40	GAN	PG-HP	50000	5000000	28625412758162949323033	74.600	2	2	3690733070112361	2	0.178

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	4B99C14446044745	0.160
2018-05-13T20:26:17	kkmrkkblmbrbk	old	4B99C14446044745	0.160

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-02T01:18:45

CrypticClue

Manual testing

28625412758162949323033

B21C36D20BF1EC97

2020-07-03T00:50:37

marssystems

SYSTEM01

28625412758162949323033

B21C36D20BF1EC97

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 160000, B2 = 3640000 (P-1 stage 2)

B1 = 160000 (P-1 stage 1)

B1 = 40000, B2 = 630000 (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

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-03T00:50:37+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