M2253037 Mersenne number exponent details

is 2 ^2253037 - 1

has 678232 decimal digits

takes 0.148 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	26.4553	67.6471%	589050	5890500	0.0837	3.9637%	26.5390	68.9294%	1.2824%
PrimeNet	2⁵⁸	0.0170	62.0690%	10000	190000	0.0019	2.9169%	0.0189	63.1754%	1.1064%
GPU72	2⁶²	0.2727	64.5161%	12000	190000	0.0021	1.7052%	0.2747	65.1212%	0.6051%
Difference	+6	+26.1827	+3.1309%	+577050	+5700500	+0.0816	+2.2585%	+26.2643	+3.8082%	+3.8082%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2253037	404744064963341851721	21	68.456	89821885961780 2² × 5 × 7 × 103 × 6228979609	2020-06-01	103	6228979609	36.908	32.355	60.430

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-03T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.228%
2010-11-06T12:26:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.200%
2010-11-14T20:17:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.257%
2010-11-23T10:46:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.676%
2011-01-14T21:29:00	Oscar Östlin		85000	1636250		-		-	-	0.016	-	-	2.195%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	113488	113488		-		-	-	0.011	-	-	0.869%
2014-10-03T21:04:00	Jocelyn Larouche	Manual testing	141976	141976		-		-	-	0.014	-	-	0.987%
2016-01-19T00:49:58	Jocelyn Larouche	Manual testing	589050	5890500	6	-		-	-	0.084	-	-	3.964%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-11T00:00:00	DL	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2016-02-23T16:29:10	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.051	-	-
2009-01-11T11:47:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.068	-	-
2012-05-04T12:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.136	-	-
2013-01-23T08:24:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.436	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.871	-	-
2015-03-10T10:44:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.658	-	-
2015-10-27T09:37:31	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.317	-	-
2017-01-05T21:20:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.633	-	-
2019-05-20T13:24:27	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.27	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.183 GHz-days
Estimated T-Level:	3.600

Digits	B1	Curves	Complete	FacMiss
20	11000	72 / 100	0.720	48.499%
25	50000	72 / 280	0.257	77.290%

New Calculation Method

Total ECM effort:	6.183 GHz-days
Estimated T-Level:	3.600

Digits	B1	Complete	FacMiss
20	11000	2.323	9.802%
25	50000	0.210	81.066%
30	250000	0.013	98.716%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	5.926
50000	5000000	404744064963341851721	3	0.258

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-25T03:31:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.258
2009-12-31T11:55:00	SubPrime	stor	50000	5000000						3	0.258
2011-10-22T02:43:00	Huaiyu Wu	lenovo	50000	5000000						3	0.258
2013-08-05T17:06:00	Kripke	Kripke	50000	5000000						3	0.258
2015-03-30T00:11:00	dragon325	Falken-i7-920	50000	5000000						3	0.258
2016-02-03T00:08:51	Jason U	Server7	50000	5000000						3	0.258
2016-03-30T05:11:54	Bruce	Desk6	50000	5000000						3	0.258
2016-07-18T16:40:17	Bruce	Desk6	50000	5000000						3	0.258
2016-12-05T02:49:21	Bruce	Desk6	50000	5000000						3	0.258
2017-06-30T17:13:57	Bruce	Desk6	50000	5000000						3	0.258
2017-12-14T15:27:29	Bruce	Desk6	50000	5000000						3	0.258
2018-05-21T16:33:15	Bruce	Desk6	50000	5000000						3	0.258
2019-05-05T20:01:05	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-02-22T03:44:25	Keysarecool	i9	50000	5000000						3	0.258
2020-02-28T17:27:26	mnd9	75202b	50000	5000000						3	0.258
2020-03-09T20:37:10	Nesowa	entropy_generator_2	50000	5000000						3	0.258
2020-03-13T13:21:04	kracker	O0	50000	5000000						3	0.258
2020-03-21T01:57:31	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.258
2020-04-02T04:21:54	Keysarecool	Boat_Anchor	50000	5000000						3	0.258
2020-04-15T23:50:14	Oliver Kruse	IOS-1	50000	5000000						3	0.258
2020-04-25T07:52:05	mnd9	fb	50000	5000000						3	0.258
2020-05-03T21:45:08	Brett Walker	brain	50000	5000000						3	0.258
2020-05-15T10:29:55	daveward2005	MW	50000	5000000						3	0.258
2020-06-01T04:10:54	GAN	PG	50000	5000000	404744064963341851721	68.456	3	2	4038883036044362	3	0.258

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-11T00:00:00	DL	v4_computers	C2D72B07D2C36C5B	0.148
1999-03-01T00:00:00	Ethan O'Connor	v4_computers	C2D72B07D2C36C5B	0.148
2018-04-23T06:58:08	kkmrkkblmbrbk	old	C2D72B07D2C36C5B	0.148

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-06-03T00:40:07

Oliver Kruse

Threadripper-PC

404744064963341851721

E62864960B29B5DE

2020-06-03T00:54:14

ATH

ec2-PRPCFDC

404744064963341851721

E62864960B29B5DE

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 = 589050, B2 = 5890500 (P-1 stage 2)

B1 = 589050 (P-1 stage 1)

B1 = 85000, B2 = 1636250 (P-1 stage 2)

B1 = 141976 (P-1 stage 1)

B1 = 113488 (P-1 stage 1)

B1 = 85000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-06-03T00:54:14+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