M5055133 Mersenne number exponent details

Residue

Status

L-L

9C06E141BE635BF0

double-checked

PRP

95A13B91B32C27D2

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	2⁷²	189.1807	68.0556%	1500000	45000000	0.7778	4.9521%	189.9585	69.6375%	1.5819%
PrimeNet	2⁶¹	0.0608	62.2951%	22000	500000	0.0097	3.4045%	0.0704	63.5787%	1.2837%
GPU72	2⁶⁵	1.4432	64.6154%	34000	700000	0.0141	2.4205%	1.4574	65.4719%	0.8565%
Difference	+7	+187.7375	+3.4402%	+1466000	+44300000	+0.7637	+2.5316%	+188.5012	+4.1656%	+4.1656%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

189.1807

68.0556%

1500000

45000000

0.7778

4.9521%

189.9585

69.6375%

1.5819%

PrimeNet

2⁶¹

0.0608

62.2951%

22000

500000

0.0097

3.4045%

0.0704

63.5787%

1.2837%

GPU72

2⁶⁵

1.4432

64.6154%

34000

700000

0.0141

2.4205%

1.4574

65.4719%

0.8565%

Difference

+187.7375

+3.4402%

+1466000

+44300000

+0.7637

+2.5316%

+188.5012

+4.1656%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5055133	24881947332582829814359	23	74.398	2461057635138663 3 × 11 × 761 × 1607 × 60982793	2021-10-30	1607	60982793	924.42	0.6681	1.2472

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

5055133

24881947332582829814359

74.398

2461057635138663
3 × 11 × 761 × 1607 × 60982793

2021-10-30

1607

60982793

924.42

0.6681

1.2472

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	50000	50000		-		-	-	0.010	-	-	0.326%
2009-07-29T13:18:00	harlee	P4_2600	60000	1065000		-		-	-	0.023	-	-	1.236%
2017-06-25T10:36:29	mikr	S051	1500000	45000000	12	-		-	-	0.778	-	-	4.952%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-10-30T23:36:38	ATH	5960X	2500000	92500000	2	7	24881947332582829814359	P-1	23	74.398	1.730

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-10-30T23:36:38

ATH

5960X

2500000

92500000

24881947332582829814359

P-1

74.398

1.730

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-05-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.061	-	-
2008-08-31T06:48:00	Sturle Sunde	lara	2⁶¹	2⁶²		-	-	0.061	-	-
2009-08-08T04:04:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.316	-	-
2016-02-23T16:39:07	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.194	-	-
2014-09-03T01:17:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.388	-	-
2014-09-14T19:48:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	0.739	-	-
2015-08-01T23:20:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.478	-	-
2016-05-20T16:48:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.956	-	-
2018-06-11T12:29:28	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	5.913	-	-
2021-02-08T11:47:16	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	11.83	-	-
2021-04-01T10:40:50	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	23.65	-	-
2021-04-01T10:40:50	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	47.30	-	-
2021-04-03T17:56:51	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	94.61	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Curves	Complete	FacMiss
20	11000	9 / 100	0.090	91.352%
25	50000	9 / 280	0.032	96.831%

New Calculation Method

Total ECM effort:	1.897 GHz-days
Estimated T-Level:	0.450

Digits	B1	Complete	FacMiss
20	11000	0.290	74.802%
25	50000	0.026	97.410%
30	250000	0.002	99.839%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		9	1.897

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-09-07T16:39:00	S00030	op9020-usff	50000	5000000						3	0.632
2014-06-13T19:18:00	S36049	Wolle5	50000	5000000						3	0.632
2017-07-07T19:50:21	Bruce	Desk10	50000	5000000						3	0.632

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	ANONYMOUS	v4_computers	9C06E141BE635BF0	0.701
2000-04-19T00:00:00	ANONYMOUS	v4_computers	9C06E141BE635BF0	0.701

date

userid

compid

res64

spent (GHz-days)

1998-12-13T00:00:00

ANONYMOUS

v4_computers

9C06E141BE635BF0

0.701

2000-04-19T00:00:00

ANONYMOUS

v4_computers

9C06E141BE635BF0

0.701

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 = 2500000, B2 = 92500000 (P-1 stage 2)

B1 = 1500000, B2 = 45000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 1500000 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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