M3762001 Mersenne number exponent details

Residue

Status

L-L

9FB7CFF2BBB194FE

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	7.8984	67.1642%	500000	130364850	1.1537	7.7756%	9.0521	69.7174%	2.5532%
PrimeNet	2⁶⁰	0.0408	63.3333%	17000	340000	0.0053	3.1824%	0.0461	64.5002%	1.1669%
GPU72	2⁶⁴	0.9461	65.6250%	22000	450000	0.0069	2.1119%	0.9530	66.3510%	0.7260%
Difference	+3	+6.9523	+1.5392%	+478000	+129914850	+1.1468	+5.6637%	+8.0991	+3.3664%	+3.3664%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

7.8984

67.1642%

500000

130364850

1.1537

7.7756%

9.0521

69.7174%

2.5532%

PrimeNet

2⁶⁰

0.0408

63.3333%

17000

340000

0.0053

3.1824%

0.0461

64.5002%

1.1669%

GPU72

2⁶⁴

0.9461

65.6250%

22000

450000

0.0069

2.1119%

0.9530

66.3510%

0.7260%

Difference

+6.9523

+1.5392%

+478000

+129914850

+1.1468

+5.6637%

+8.0991

+3.3664%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3762001	5103952898669668143849730297	28	92.044	678356132636550089148 2² × 3 × 7 × 523 × 40759 × 45181 × 8384891	2016-01-10	45181	8384891	349,012,227	0.0761	0.1299

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3762001

5103952898669668143849730297

92.044

678356132636550089148
2² × 3 × 7 × 523 × 40759 × 45181 × 8384891

2016-01-10

45181

8384891

349,012,227

0.0761

0.1299

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-11T19:30:00	Carsten Kossendey	durandal	20000	265000		-		-	-	0.005	-	-	1.151%
2012-04-04T14:14:00	Squeeky_Squirrel	P4_2600	110000	2035000		-		-	-	0.033	-	-	2.958%
2016-01-10T13:01:56	mikr	MSI	1600000	66000000	12		5103952898669668143849730297	28	92.044	0.778	0.790	1.556	7.951%
2022-05-17T01:12:25	Jocelyn Larouche	Manual testing	500000	130364850		-	skipped known factor: 5103952898669668143849730297	-	-	1.154	-	-	7.776%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.041	-	-
2009-03-03T17:12:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.041	-	-
2011-05-05T09:17:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.082	-	-
2012-03-23T23:44:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.424	-	-
2016-02-23T16:29:38	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.261	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.522	-	-
2015-01-25T20:42:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.993	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.346 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:	1.346 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	1.346

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-09-10T22:45:00	Gerry Snyder	blu	50000	5000000						3	0.449
2012-07-13T23:32:00	S36049	Wolle5	50000	5000000						3	0.449
2015-12-18T02:55:29	Richard Kint	Desktop	50000	5000000						3	0.449

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-10-18T00:00:00	ANONYMOUS	v4_computers	9FB7CFF2BBB194FE	0.395
1999-09-14T00:00:00	ANONYMOUS	v4_computers	9FB7CFF2BBB194FE	0.395

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:28:25

kkmrkkblmbrbk

Manual testing

5103952898669668143849730297

313F9786933F33__

2017-12-07T05:41:40

Oliver Kruse

GTX-1

5103952898669668143849730297

313F9786933F33__

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 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 1600000, B2 = 66000000 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 110000, B2 = 2035000 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 20000, B2 = 265000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

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