M1273919 Mersenne number exponent details

Residue

Status

L-L

C8095142099DD22B

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	23.3248	68.6567%	1195000	34655000	0.1387	6.2057%	23.4635	70.6018%	1.9451%
PrimeNet	2⁵⁶	0.0075	62.5000%	5500	90000	0.0005	2.4457%	0.0080	63.4172%	0.9172%
GPU72	2⁶⁰	0.1206	65.0000%	5500	36000	0.0003	0.9306%	0.1209	65.3257%	0.3257%
Difference	+7	+23.2042	+3.6567%	+1189500	+34619000	+0.1384	+5.2751%	+23.3426	+5.2761%	+5.2761%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

23.3248

68.6567%

1195000

34655000

0.1387

6.2057%

23.4635

70.6018%

1.9451%

PrimeNet

2⁵⁶

0.0075

62.5000%

5500

90000

0.0005

2.4457%

0.0080

63.4172%

0.9172%

GPU72

2⁶⁰

0.1206

65.0000%

5500

36000

0.0003

0.9306%

0.1209

65.3257%

0.3257%

Difference

+23.2042

+3.6567%

+1189500

+34619000

+0.1384

+5.2751%

+23.3426

+5.2761%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1273919	117903828000904646513473	24	76.642	46276030109019744 2⁵ × 3² × 11 × 17 × 59 × 14563641811	2014-03-15	59	14563641811	12,700	36.465	68.107

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1273919

117903828000904646513473

76.642

46276030109019744
2⁵ × 3² × 11 × 17 × 59 × 14563641811

2014-03-15

14563641811

12,700

36.465

68.107

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2013-10-07T16:33:00	David Campeau	i5-2500k	1195000	34655000		-		-	-	0.139	-	-	6.206%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-02-24T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.240%

2013-10-07T16:33:00

David Campeau

i5-2500k

1195000

34655000

0.139

-

-

6.206%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.008	-	-
2001-11-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2003-06-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.030	-	-
2022-03-07T17:32:05	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.090	-	-
2009-02-18T07:08:00	Sturle Sunde	eames.ifi	2⁶⁰	2⁶¹		-	-	0.121	-	-
2012-09-15T18:40:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.241	-	-
2012-10-18T21:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.771	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.677 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	300 / 100	3.000	4.904%
25	50000	300 / 280	1.071	34.186%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	20.677 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.231	0.000%
25	50000	1.354	25.824%
30	250000	0.113	89.331%
35	1000000	0.008	99.237%

ECM Summary

B1	B2	factor	curves	GHz-days
		117903828000904646513473	1	0.00000e+0
50000	5000000		250	9.61
250000	35000000		50	11.06

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-11T16:05:00	James Heinrich	WHS	50000	5000000						1	0.038
2008-08-30T02:05:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-02-07T18:22:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-07-28T03:57:00	wuxiao	DNE_Black_Sheep	50000	5000000						3	0.115
2009-10-20T06:46:00	SubPrime	c2d0	50000	5000000						3	0.115
2010-04-04T09:05:00	sannerud.com	snap1	50000	5000000						3	0.115
2011-01-07T17:35:00	eteo	stephanie	50000	5000000						3	0.115
2011-10-23T23:26:00	Andriy Makukha	freehost	50000	5000000						3	0.115
2012-07-15T15:25:00	soldake		50000	5000000						3	0.115
2013-02-07T20:29:00	OS1	Tina	50000	5000000						3	0.115
2013-10-29T06:46:00	OS1	Tina	50000	5000000						3	0.115
2014-03-01T23:24:00	Bruce	snowflake	50000	5000000						3	0.115
2014-03-15T13:57:00	Bruce	snowflake			117903828000904646513473	76.642		1		1	-
2018-01-19T13:26:19	TJAOI	Manual testing	50000	5000000						216	8.307
2021-05-21T15:31:10	TJAOI	Manual testing	250000	35000000						50	11.06

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 = 1195000, B2 = 34655000 (P-1 stage 2)

B1 = 1195000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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