M2378737 Mersenne number exponent details

Residue

Status

L-L

D7907CDA294FC46D

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	12.4915	67.1642%	3000000	60000000	0.5981	7.8342%	13.0895	69.7366%	2.5724%
PrimeNet	2⁵⁹	0.0323	62.7119%	10000	170000	0.0018	2.4755%	0.0341	63.6349%	0.9231%
GPU72	2⁶³	0.6710	65.0794%	10000	140000	0.0017	1.2725%	0.6726	65.5237%	0.4444%
Difference	+4	+11.8205	+2.0848%	+2990000	+59860000	+0.5964	+6.5617%	+12.4169	+4.2129%	+4.2129%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

12.4915

67.1642%

3000000

60000000

0.5981

7.8342%

13.0895

69.7366%

2.5724%

PrimeNet

2⁵⁹

0.0323

62.7119%

10000

170000

0.0018

2.4755%

0.0341

63.6349%

0.9231%

GPU72

2⁶³

0.6710

65.0794%

10000

140000

0.0017

1.2725%

0.6726

65.5237%

0.4444%

Difference

+11.8205

+2.0848%

+2990000

+59860000

+0.5964

+6.5617%

+12.4169

+4.2129%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2378737	432422087262164069263190161	27	88.483	90893210821995888840 2³ × 3 × 5 × 19 × 21557 × 864439 × 2139311	2015-10-13	864439	2139311	37,304,318	0.0915	0.1723

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2378737

432422087262164069263190161

88.483

90893210821995888840
2³ × 3 × 5 × 19 × 21557 × 864439 × 2139311

2015-10-13

864439

2139311

37,304,318

0.0915

0.1723

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.287%
2010-11-07T17:07:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.243%
2010-11-15T22:51:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.310%
2010-12-28T03:36:00	markr	tiny	100000	2050000		-		-	-	0.020	-	-	2.721%
2014-09-10T00:51:00	Jocelyn Larouche	Manual testing	126983	126983		-		-	-	0.012	-	-	1.074%
2015-10-12T17:08:51	mikr	MSI	3000000	60000000			432422087262164069263190161	27	88.483	0.294	0.321	0.588	7.834%
2018-09-28T16:24:46	alpertron	Manual testing	2000000	60000000	12	-	skipped known factor: 432422087262164069263190161	-	-	0.505	-	-	7.608%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-09T16:37:54	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.065	-	-
2009-01-15T02:07:00	Sturle Sunde	goober.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-31T20:06:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.129	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.413	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.825	-	-
2015-03-09T12:35:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.571	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.334 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.334 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.334

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-26T18:08:00	oodaira	Win02	50000	5000000						3	0.267
2010-02-12T05:10:00	SubPrime	abd0	50000	5000000						3	0.267
2012-01-25T22:02:00	S36049	Wolle5	50000	5000000						3	0.267
2013-11-19T16:17:00	Andy Incline	Office-PC	50000	5000000						3	0.267
2015-06-22T19:09:00	guru	w6	50000	5000000						3	0.267

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	D7907CDA294FC46D	0.161

date

userid

compid

res64

spent (GHz-days)

1999-03-15T00:00:00

ANONYMOUS

v4_computers

D7907CDA294FC46D

0.161

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:29:15

alpertron

Manual testing

432422087262164069263190161

2DA1569FAA74D9__

2017-11-02T06:03:08

Oliver Kruse

GTX-3

432422087262164069263190161

2DA1569FAA74D9__

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 = 60000000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 100000, B2 = 2050000 (P-1 stage 2)

B1 = 126983 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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