M2959949 Mersenne number exponent details

Residue

Status

L-L

55025905C3378144

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	2⁶⁸	20.1371	67.6471%	1000000	20000000	0.2512	5.5458%	20.3883	69.4413%	1.7942%
PrimeNet	2⁶⁰	0.0519	63.3333%	12000	220000	0.0029	2.5089%	0.0548	64.2533%	0.9199%
GPU72	2⁶⁴	1.2025	65.6250%	12000	200000	0.0027	1.3475%	1.2052	66.0882%	0.4632%
Difference	+4	+18.9346	+2.0221%	+988000	+19800000	+0.2484	+4.1983%	+19.1831	+3.3531%	+3.3531%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.1371

67.6471%

1000000

20000000

0.2512

5.5458%

20.3883

69.4413%

1.7942%

PrimeNet

2⁶⁰

0.0519

63.3333%

12000

220000

0.0029

2.5089%

0.0548

64.2533%

0.9199%

GPU72

2⁶⁴

1.2025

65.6250%

12000

200000

0.0027

1.3475%

1.2052

66.0882%

0.4632%

Difference

+18.9346

+2.0221%

+988000

+19800000

+0.2484

+4.1983%

+19.1831

+3.3531%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2959949	27224021610429027080527	23	74.527	4598731533960387 3⁵ × 67 × 73 × 3869315299	2020-09-24	243	3869315299	1,501.5	26.016	48.591

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2959949

27224021610429027080527

74.527

4598731533960387
3⁵ × 67 × 73 × 3869315299

2020-09-24

243

3869315299

1,501.5

26.016

48.591

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	-	-	0.247%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.146%
2010-10-31T18:45:00	markr	tiny	95000	1995000		-		-	-	0.024	-	-	2.458%
2015-05-08T13:54:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.546%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.052	-	-
2009-02-14T20:49:00	Sturle Sunde	graun.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-09T10:40:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.104	-	-
2013-01-07T13:49:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.332	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.663	-	-
2015-04-29T14:58:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.262	-	-
2016-02-26T10:03:34	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.525	-	-
2017-12-03T16:23:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.049	-	-
2018-12-24T00:53:35	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.10	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.549 GHz-days
Estimated T-Level:	1.100

Digits	B1	Curves	Complete	FacMiss
20	11000	22 / 100	0.220	80.163%
25	50000	22 / 280	0.079	92.431%

New Calculation Method

Total ECM effort:	2.549 GHz-days
Estimated T-Level:	1.100

Digits	B1	Complete	FacMiss
20	11000	0.710	49.180%
25	50000	0.064	93.787%
30	250000	0.004	99.606%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	2.086
50000	5000000	27224021610429027080527	4	0.463

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-01T14:08:00	Lupo	yorick	50000	5000000						3	0.348
2011-04-29T06:42:00	he4var		50000	5000000						3	0.348
2013-07-13T13:56:00	Bruce	E6510	50000	5000000						3	0.348
2016-01-04T13:35:39	Bruce	Desk7	50000	5000000						3	0.348
2017-06-14T18:22:35	bayanne	iMac	50000	5000000						3	0.348
2019-10-26T08:25:26	Idgo	Pentium_Desktop	50000	5000000						3	0.348
2020-09-24T03:10:14	GAN	KL-SCH09	50000	5000000	27224021610429027080527	74.527	4	2	6293455149965760	4	0.463

date	userid	compid	res64	spent (GHz-days)
1999-12-30T00:00:00	ANONYMOUS	v4_computers	55025905C3378144	0.252
2018-10-14T10:16:41	kkmrkkblmbrbk	old	55025905C3378144	0.252

date

userid

compid

res64

spent (GHz-days)

1999-12-30T00:00:00

ANONYMOUS

v4_computers

55025905C3378144

0.252

2018-10-14T10:16:41

kkmrkkblmbrbk

old

55025905C3378144

0.252

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-09-25T02:38:47

Yuji Hasegawa

vj22m

27224021610429027080527

469BC61B92385778

2020-09-25T14:44:36

kutens

sol

27224021610429027080527

469BC61B92385778

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 = 95000, B2 = 1995000 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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