M3095959 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

66BF4F78295D7C__

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	19.2525	67.6471%	3000000	100000000	1.0224	8.0468%	20.2749	70.2504%	2.6034%
PrimeNet	2⁶⁰	0.0496	63.3333%	12000	220000	0.0029	2.5298%	0.0525	64.2609%	0.9276%
GPU72	2⁶⁴	1.1497	65.6250%	14000	240000	0.0032	1.5067%	1.1529	66.1429%	0.5179%
Difference	+4	+18.1028	+2.0221%	+2986000	+99760000	+1.0192	+6.5401%	+19.1220	+4.1075%	+4.1075%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.2525

67.6471%

3000000

100000000

1.0224

8.0468%

20.2749

70.2504%

2.6034%

PrimeNet

2⁶⁰

0.0496

63.3333%

12000

220000

0.0029

2.5298%

0.0525

64.2609%

0.9276%

GPU72

2⁶⁴

1.1497

65.6250%

14000

240000

0.0032

1.5067%

1.1529

66.1429%

0.5179%

Difference

+18.1028

+2.0221%

+2986000

+99760000

+1.0192

+6.5401%

+19.1220

+4.1075%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3095959	930474509145145121774338871	27	89.588	150272421105244791965 5 × 23 × 31 × 401 × 105117585492961	2021-01-04	401	105117585492961	78,930,762	706,787	1,320,082

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3095959

930474509145145121774338871

89.588

150272421105244791965
5 × 23 × 31 × 401 × 105117585492961

2021-01-04

401

105117585492961

78,930,762

706,787

1,320,082

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T00:58:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.762%
2011-08-17T02:08:00	harlee	P4_2600	100000	2125000		-		-	-	0.026	-	-	2.537%
2016-04-17T17:42:41	Jocelyn Larouche	Manual testing	200000	6167043	6	-		-	-	0.065	-	-	3.625%
2018-05-20T09:52:24	mikr	MSI	3000000	100000000	12	-		-	-	1.022	-	-	8.047%
2022-02-20T22:18:38	Jocelyn Larouche	Manual testing	1000000	128282700		-		-	-	0.979	-	-	7.554%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.025	-	-
2001-07-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-12T21:42:00	Sturle Sunde	goldiek.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2011-12-05T23:24:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.099	-	-
2013-01-07T13:56:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.317	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.634	-	-
2015-02-07T18:29:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.207	-	-
2015-06-11T22:04:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.414	-	-
2017-05-18T12:32:23	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.827	-	-
2018-08-19T20:55:20	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	9.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.503 GHz-days
Estimated T-Level:	1.500

Digits	B1	Curves	Complete	FacMiss
20	11000	30 / 100	0.300	73.970%
25	50000	30 / 280	0.107	89.823%

New Calculation Method

Total ECM effort:	3.503 GHz-days
Estimated T-Level:	1.500

Digits	B1	Complete	FacMiss
20	11000	0.968	37.994%
25	50000	0.087	91.625%
30	250000	0.005	99.463%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	3.386
50000	5000000	930474509145145121774338871	1	0.117

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-26T23:51:00	Smurgs	23-3-15	50000	5000000						3	0.350
2011-07-11T03:58:00	sannerud.com	Jim2010	50000	5000000						3	0.350
2013-12-01T04:12:00	Richard Kint	xps	50000	5000000						3	0.350
2016-05-05T23:14:27	Ismo Laitela		50000	5000000						3	0.350
2017-12-27T07:03:54	Claude Portenier	Petit-Idiot	50000	5000000						3	0.350
2020-10-25T23:45:13	nordi	sweet16	50000	5000000						7	0.817
2020-11-29T17:00:50	RIHATEC	i7-3770K	50000	5000000						7	0.817
2021-01-04T19:27:13	MarkS	desktop-i7	50000	5000000	930474509145145121774338871	89.588	1	2	8574575159633698	1	0.117

date	userid	compid	res64	spent (GHz-days)
1999-06-06T00:00:00	ANONYMOUS	v4_computers	5E7B1C28F92884__	0.264

date

userid

compid

res64

spent (GHz-days)

1999-06-06T00:00:00

ANONYMOUS

v4_computers

5E7B1C28F92884__

0.264

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 1000000, B2 = 128282700 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 200000, B2 = 6167043 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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