M3027527 Mersenne number exponent details

Residue

Status

L-L

238F7F7649B8D42D

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	19.6876	67.6471%	1000000	119912100	0.9229	7.4627%	20.6106	70.0615%	2.4144%
PrimeNet	2⁶⁰	0.0507	63.3333%	12000	220000	0.0029	2.5194%	0.0536	64.2571%	0.9238%
GPU72	2⁶⁴	1.1757	65.6250%	13000	220000	0.0030	1.4289%	1.1787	66.1162%	0.4912%
Difference	+4	+18.5120	+2.0221%	+987000	+119692100	+0.9200	+6.0339%	+19.4319	+3.9453%	+3.9453%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.6876

67.6471%

1000000

119912100

0.9229

7.4627%

20.6106

70.0615%

2.4144%

PrimeNet

2⁶⁰

0.0507

63.3333%

12000

220000

0.0029

2.5194%

0.0536

64.2571%

0.9238%

GPU72

2⁶⁴

1.1757

65.6250%

13000

220000

0.0030

1.4289%

1.1787

66.1162%

0.4912%

Difference

+18.5120

+2.0221%

+987000

+119692100

+0.9200

+6.0339%

+19.4319

+3.9453%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3027527	138857589350772761087	21	66.912	22932510486409 21317 × 1075785077	2009-04-10	21317	1075785077	7.4948	7.2358	13.510

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3027527

138857589350772761087

66.912

22932510486409
21317 × 1075785077

2009-04-10

21317

1075785077

7.4948

7.2358

13.510

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.147%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.248%
2020-12-19T21:21:04	Jocelyn Larouche	Manual testing	302752	3027527	6	-		-	-	0.056	-	-	3.275%
2022-01-22T13:04:25	Jocelyn Larouche	Manual testing	1000000	119912100		-		-	-	0.923	-	-	7.463%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.051	-	-
2009-01-30T08:02:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.051	-	-
2022-03-11T19:04:00	LordJulius	Manual testing	2⁶¹	2⁶³		-	-	0.426	-	-
2022-03-11T19:04:00	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.648	-	-
2022-03-11T19:04:00	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	1.234	-	-
2022-03-11T19:04:00	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.468	-	-
2022-03-11T19:04:00	LordJulius	Manual testing	2⁶⁶	2⁶⁷	138857589350772761087	66.912	21	2.617	0.523	5.311
2021-03-20T11:55:02	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.87	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		138857589350772761087	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-10T10:57:00	Sid & Andy	Slinky			138857589350772761087	66.912		1		1	-

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	238F7F7649B8D42D	0.258

date

userid

compid

res64

spent (GHz-days)

1999-06-26T00:00:00

ANONYMOUS

v4_computers

238F7F7649B8D42D

0.258

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-27T21:13:09

Oliver Kruse

GTX-3

138857589350772761087

B6501513C4D155__

2017-12-10T16:46:35

kkmrkkblmbrbk

c4.xlarge

138857589350772761087

B6501513C4D155__

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 = 119912100 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 302752, B2 = 3027527 (P-1 stage 2)

B1 = 302752 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

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