M7231261 Mersenne number exponent details

Residue

Status

L-L

00991431AD4BE8D4

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	2⁷³	264.5243	68.4932%	16000000	16143964200	282.8855	12.6378%	547.4098	72.4749%	3.9818%
Target	2⁶⁷	4.1091	65.6716%	45000	1000000	0.0307	2.3121%	4.1398	66.4654%	0.7937%
Difference	+6	+260.4152	+2.8215%	+15955000	+16142964200	+282.8548	+10.3257%	+543.2700	+6.0096%	+3.1881%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

264.5243

68.4932%

16000000

16143964200

282.8855

12.6378%

547.4098

72.4749%

3.9818%

Target

2⁶⁷

4.1091

65.6716%

45000

1000000

0.0307

2.3121%

4.1398

66.4654%

0.7937%

Difference

+260.4152

+2.8215%

+15955000

+16142964200

+282.8548

+10.3257%

+543.2700

+6.0096%

+3.1881%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
7231261	5877492607698540401358690371584903629647	40	132.110	406394722006199223161678880874643 11 × 17 × 1123 × 1223 × 6763 × 57349 × 12846209 × 317585027	2023-01-01	12846209	317585027	1.803e+10	9.3113	10.218

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

7231261

5877492607698540401358690371584903629647

132.110

406394722006199223161678880874643
11 × 17 × 1123 × 1223 × 6763 × 57349 × 12846209 × 317585027

2023-01-01

12846209

317585027

1.803e+10

9.3113

10.218

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-10T00:00:00	pgnn	v4_computers	35000	35000		-		-	-	0.011	-	-	0.227%
2012-01-18T06:25:00	Carsten Kossendey	mother	460000	14030000		-		-	-	0.379	-	-	3.239%
2022-11-28T20:58:21	yoyorocks1	Manual testing	16000000	16143964200			5877492607698540401358690371584903629647	40	132.110	282.9	3.154	565.8	12.638%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-07-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.085	-	-
2002-02-10T00:00:00	pgnn	v4_computers	2¹	2⁶³		-	-	0.221	-	-
2013-11-03T11:13:00	Nesowa	Manual testing	2⁶³	2⁶⁴		-	-	0.272	-	-
2013-11-14T12:28:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.517	-	-
2015-06-16T01:49:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	1.033	-	-
2016-10-13T23:59:18	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.067	-	-
2018-07-23T10:43:50	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	4.134	-	-
2020-03-27T10:19:01	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	8.267	-	-
2021-08-19T16:11:16	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	16.53	-	-
2021-08-24T16:12:15	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	33.07	-	-
2021-09-28T15:11:03	SRBase	Manual testing	2⁷¹	2⁷²		-	-	66.14	-	-
2021-12-27T11:35:18	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	132.3	-	-

ECM factoring results:

Total ECM effort:	1.989 GHz-days
Estimated T-Level:	1.154

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.989

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2012-11-14T22:45:00	Gerry Snyder	blu	50000	5000000						3	0.995
2017-11-21T16:42:44	mpickering	bellerophon	50000	5000000						3	0.995

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	Stephen Wood	v4_computers	00991431AD4BE8D4	1.577
2002-03-24T00:00:00	pgnn	v4_computers	00991431AD4BE8D4	1.577

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 = 16000000, B2 = 16143964200 (P-1 stage 2)

B1 = 16000000 (P-1 stage 1)

B1 = 460000, B2 = 14030000 (P-1 stage 2)

B1 = 460000 (P-1 stage 1)

B1 = 35000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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