M1915931 Mersenne number exponent details

Residue

Status

L-L

5F3790BC5F37F355

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	15.5089	68.6567%	8000000	320000000	1.9665	10.4704%	17.4753	71.9385%	3.2818%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0916%	0.0114	64.2969%	1.1390%
GPU72	2⁶¹	0.1603	65.5738%	10000	170000	0.0015	1.7608%	0.1618	66.1799%	0.6062%
Difference	+6	+15.3485	+3.0829%	+7990000	+319830000	+1.9650	+8.7096%	+17.3135	+5.7585%	+5.7585%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5089

68.6567%

8000000

320000000

1.9665

10.4704%

17.4753

71.9385%

3.2818%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0916%

0.0114

64.2969%

1.1390%

GPU72

2⁶¹

0.1603

65.5738%

10000

170000

0.0015

1.7608%

0.1618

66.1799%

0.6062%

Difference

+15.3485

+3.0829%

+7990000

+319830000

+1.9650

+8.7096%

+17.3135

+5.7585%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1915931	232890736798393288082113	24	77.624	60777433216121376 2⁵ × 3 × 19 × 550663 × 60510623	2017-12-17	550663	60510623	16,723	0.3003	0.4844
1915931	147500872695956741672611571777	30	96.897	38493263247986681585248 2⁵ × 7² × 277 × 431 × 3566149 × 57660997	2017-12-17	3566149	57660997	8.427e+9	0.5124	0.5709

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1915931

232890736798393288082113

77.624

60777433216121376
2⁵ × 3 × 19 × 550663 × 60510623

2017-12-17

550663

60510623

16,723

0.3003

0.4844

1915931

147500872695956741672611571777

96.897

38493263247986681585248
2⁵ × 7² × 277 × 431 × 3566149 × 57660997

2017-12-17

3566149

57660997

8.427e+9

0.5124

0.5709

exponent	prime factors	composite factor	digits	bits*
1915931	232890736798393288082113 147500872695956741672611571777	34351586920567376539002446442708426138850186769324 801	53	174.521

exponent

prime factors

composite factor

digits

bits*

1915931

232890736798393288082113
147500872695956741672611571777

34351586920567376539002446442708426138850186769324
801

174.521

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-08-18T23:56:00	kurly	slice	1000000	30000000		-		-	-	0.203	-	-	6.224%
2017-12-17T11:25:37	mikr	S062	8000000	320000000	12		232890736798393288082113 147500872695956741672611571777	53	174.521	1.966	0.208	3.933	10.470%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2009-05-31T13:57:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.080	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.160	-	-
2011-07-17T18:55:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.833	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.512	-	-
2015-05-16T20:58:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.025	-	-
2015-05-16T20:58:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	1.950	-	-
2015-10-02T08:43:13	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.900	-	-
2017-03-15T08:26:29	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.801	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.456 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	21.456 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.055	0.012%
25	50000	0.805	44.709%
30	250000	0.050	95.132%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		46	3.194
50000	8000000		212	18.26

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-07T18:32:00	Jorge Flora	PC_01b	50000	5000000						3	0.208
2009-08-07T16:15:00	Conductor	home	50000	5000000						3	0.208
2010-12-04T19:30:00	Lupo	yorick	50000	5000000						3	0.208
2012-11-04T12:58:00	Syntony	Geomancer	50000	5000000						3	0.208
2013-12-02T18:18:00	Sara	Sara	50000	5000000						3	0.208
2014-12-08T01:35:00	Chris Smith	starcraft2	50000	5000000						3	0.208
2015-09-05T18:23:00	Sara	Sara	50000	5000000						3	0.208
2016-04-16T06:16:44	Jason U	Server7	50000	5000000						3	0.208
2016-06-16T19:53:03	Bruce	Desk6	50000	5000000						3	0.208
2016-08-28T06:30:13	Bruce	test	50000	5000000						3	0.208
2017-02-05T18:25:12	Bruce	Desk6	50000	5000000						3	0.208
2017-07-31T00:27:22	Bruce	Desk6	50000	5000000						3	0.208
2017-12-12T16:07:02	Bruce	Desk6	50000	5000000						3	0.208
2022-01-25T11:46:57	TJAOI	Manual testing	50000	8000000						212	18.26
2022-01-25T15:25:43	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	5F3790BC5F37F355	0.104
2015-07-14T15:04:00	MadPoo	Manual testing	5F3790BC5F37F355	0.104

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

5F3790BC5F37F355

0.104

2015-07-14T15:04:00

MadPoo

Manual testing

5F3790BC5F37F355

0.104

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 = 8000000, B2 = 320000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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