M78 737 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

Cofactor is a certified prime

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	100000000	2000000000	0.4427	40.3335%	0.4427	40.3335%
Target	2⁴⁴	0.0000	61.3636%	500	50000	0.0000	2.3207%	0.0000	62.2603%
Difference	-44	0.0000	-61.3636%	+99999500	+1999950000	+0.4426	+38.0128%	+0.4426	-21.9268%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

100000000

2000000000

0.4427

40.3335%

0.4427

40.3335%

Target

2⁴⁴

0.0000

61.3636%

500

50000

0.0000

2.3207%

0.0000

62.2603%

Difference

-44

0.0000

-61.3636%

+99999500

+1999950000

+0.4426

+38.0128%

+0.4426

-21.9268%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
78737	23714605956035916529	20	64.362	150593786631672 2³ × 3 × 19 × 163 × 179 × 11318831	2014-04-23	179	11318831	68.131	0.0013	0.0025
78737	67059801476528402969297162417	29	95.759	425846815833270272992984 2³ × 79 × 673808252900744102837	2019-04-07	79	673808252900744102837	1.166e+11	7.985e+10	1.491e+11
78737	hide decimal representation P23654 click to show decimal representation	23,654	78,576.878		2019-04-07

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

78737

23714605956035916529

64.362

150593786631672
2³ × 3 × 19 × 163 × 179 × 11318831

2014-04-23

179

11318831

68.131

0.0013

0.0025

78737

67059801476528402969297162417

95.759

425846815833270272992984
2³ × 79 × 673808252900744102837

2019-04-07

673808252900744102837

1.166e+11

7.985e+10

1.491e+11

78737

P23654

click to show decimal representation

23,654

78,576.878

2019-04-07

exponent	prime factors	composite factor	digits	bits*
78737	23714605956035916529 67059801476528402969297162417	1590296767505866614563328548192658003295567890593	49	160.122

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-12-19	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 23714605956035916529	-	-	0.443	-	-	40.333%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-12-19

kkmrkkblmbrbk

Manual testing

100000000

2000000000

skipped known factor: 23714605956035916529

0.443

-

-

40.333%

ECM factoring results:

Total ECM effort:	8.084 GHz-days
Estimated T-Level:	30.714

Digits	B1	Complete	FacMiss
20	11000	80.324	0.000%
25	50000	12.493	0.000%
30	250000	1.477	22.837%
35	1000000	0.143	86.689%
40	3000000	0.012	98.830%

ECM Summary

B1	B2	factor	curves	GHz-days
11000	1100000		30	0.010
50000	5000000		274	0.429
250000	25000000		585	4.577
1000000	100000000		96	3.005
1000000	100000000	67059801476528402969297162417	2	0.063

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

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-22	Matthias Wurtinger	WUR_E6600	11000	1100000						30	0.010
2010-04-26	James Hintz	18_012210	50000	5000000						11	0.017
2011-01-09	James Hintz	NEW_OMFG	50000	5000000						2	0.003
2011-01-20	James Hintz	mom3	50000	5000000						10	0.016
2011-02-13	James Hintz	OMFG	50000	5000000						10	0.016
2011-02-23	James Hintz	NEW_OMFG	50000	5000000						10	0.016
2011-05-13	James Hintz	NEW_OMFG	50000	5000000						50	0.078
2014-07-11	TJAOI	Manual testing	50000	5000000						181	0.283
2017-02-15	kkmrkkblmbrbk	x116xl	250000	25000000						585	4.577
2018-11-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2018-11-28	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2018-12-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2018-12-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2018-12-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2018-12-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2018-12-15	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2018-12-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2018-12-22	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2018-12-26	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2018-12-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-01-03	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-01-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-01-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2019-01-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-01-17	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2019-01-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2019-01-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2019-02-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-02-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-02-10	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-02-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-02-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2019-02-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2019-02-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2019-03-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-03-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-03-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-03-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.094
2019-03-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-03-28	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.094
2019-04-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.094
2019-04-06	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000	67059801476528402969297162417	95.759	2	2		2	0.063