M2937269 Mersenne number exponent details

Residue

Status

L-L

9237C0FB61EE4D5A

double-checked

PRP

1B030EB147AD742D

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.2926	67.6471%	1000000	20000000	0.2512	5.5410%	20.5438	69.4397%	1.7927%
PrimeNet	2⁵⁹	0.0261	62.7119%	13000	260000	0.0033	3.0713%	0.0294	63.8571%	1.1452%
GPU72	2⁶³	0.5434	65.0794%	17000	300000	0.0040	1.9460%	0.5474	65.7589%	0.6796%
Difference	+5	+19.7493	+2.5677%	+983000	+19700000	+0.2472	+3.5950%	+19.9964	+3.6808%	+3.6808%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.2926

67.6471%

1000000

20000000

0.2512

5.5410%

20.5438

69.4397%

1.7927%

PrimeNet

2⁵⁹

0.0261

62.7119%

13000

260000

0.0033

3.0713%

0.0294

63.8571%

1.1452%

GPU72

2⁶³

0.5434

65.0794%

17000

300000

0.0040

1.9460%

0.5474

65.7589%

0.6796%

Difference

+19.7493

+2.5677%

+983000

+19700000

+0.2472

+3.5950%

+19.9964

+3.6808%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2937269	359450499498917337283033	24	78.250	61187875454872764 2² × 3⁴ × 13 × 89 × 163225123123	2020-12-11	89	163225123123	22,844	1,097.5	2,049.8

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2937269

359450499498917337283033

78.250

61187875454872764
2² × 3⁴ × 13 × 89 × 163225123123

2020-12-11

163225123123

22,844

1,097.5

2,049.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.246%
2010-11-08T03:20:00	markr	tiny	105000	2283750		-		-	-	0.028	-	-	2.585%
2015-04-29T15:00:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.541%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:25	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-13T23:25:00	Sturle Sunde	kinner.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2012-01-01T00:37:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.334	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.668	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.272	-	-
2016-02-23T16:36:50	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.544	-	-
2017-11-24T17:10:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.088	-	-
2018-12-22T00:20:03	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.18	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.092 GHz-days
Estimated T-Level:	2.200

Digits	B1	Curves	Complete	FacMiss
20	11000	44 / 100	0.440	64.261%
25	50000	44 / 280	0.157	85.434%

New Calculation Method

Total ECM effort:	5.092 GHz-days
Estimated T-Level:	2.200

Digits	B1	Complete	FacMiss
20	11000	1.419	24.187%
25	50000	0.128	87.961%
30	250000	0.008	99.213%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	4.513
50000	5000000	359450499498917337283033	5	0.579

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-29T20:16:00	James Hintz	18_060209	50000	5000000						3	0.347
2011-04-12T23:49:00	Scott Crawford	Jane	50000	5000000						3	0.347
2013-06-27T13:01:00	Bruce	E6510	50000	5000000						3	0.347
2015-12-29T09:03:56	Bruce	Desk7	50000	5000000						3	0.347
2017-07-30T10:41:39	bayanne	iMac	50000	5000000						3	0.347
2019-09-06T22:19:59	Idgo	Pentium_Desktop	50000	5000000						3	0.347
2020-09-06T20:03:44	lycorn	colab_A	50000	5000000						7	0.810
2020-10-08T13:41:44	mnd9	27016b	50000	5000000						7	0.810
2020-11-06T05:49:04	Nesowa	entropy_generator_2	50000	5000000						7	0.810
2020-12-11T12:54:43	Keysarecool	Boat_Anchor	50000	5000000	359450499498917337283033	78.250	5	2	6804739480219109	5	0.579

date	userid	compid	res64	spent (GHz-days)
1999-05-23T00:00:00	ANONYMOUS	v4_computers	9237C0FB61EE4D5A	0.250
2018-10-09T11:12:32	kkmrkkblmbrbk	old	9237C0FB61EE4D5A	0.250

date

userid

compid

res64

spent (GHz-days)

1999-05-23T00:00:00

ANONYMOUS

v4_computers

9237C0FB61EE4D5A

0.250

2018-10-09T11:12:32

kkmrkkblmbrbk

old

9237C0FB61EE4D5A

0.250

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

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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