M8423879 Mersenne number exponent details

Residue

Status

L-L

7BA4995E461E3AEB

double-checked

PRP

E752A99366F83FEE

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	113.5265	66.6667%	1023734	30712007	1.0000	4.6970%	114.5265	68.2323%	1.5657%
PrimeNet	2⁶⁴	0.4225	62.5000%	34000	900000	0.0307	3.1759%	0.4533	63.6909%	1.1909%
GPU72	2⁶⁸	7.0757	64.7059%	50000	1100000	0.0406	2.1891%	7.1163	65.4785%	0.7726%
Difference	+4	+106.4508	+1.9608%	+973734	+29612007	+0.9594	+2.5079%	+107.4102	+2.7538%	+2.7538%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

113.5265

66.6667%

1023734

30712007

1.0000

4.6970%

114.5265

68.2323%

1.5657%

PrimeNet

2⁶⁴

0.4225

62.5000%

34000

900000

0.0307

3.1759%

0.4533

63.6909%

1.1909%

GPU72

2⁶⁸

7.0757

64.7059%

50000

1100000

0.0406

2.1891%

7.1163

65.4785%

0.7726%

Difference

+106.4508

+1.9608%

+973734

+29612007

+0.9594

+2.5079%

+107.4102

+2.7538%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8423879	30428961909571209589793	23	74.688	1806113425274224 2⁴ × 11 × 276977 × 37050037	2021-12-05	276977	37050037	566.64	0.8634	1.4274

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8423879

30428961909571209589793

74.688

1806113425274224
2⁴ × 11 × 276977 × 37050037

2021-12-05

276977

37050037

566.64

0.8634

1.4274

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-10-07T00:00:00	Team Prime Rib	v4_computers	45000	675000		-		-	-	0.030	-	-	1.099%
2012-07-26T12:21:00	bcp19	Toshiba-740Q	100000	1825000		-		-	-	0.073	-	-	1.762%
2021-12-05T10:57:56	GdS	Manual testing	1023734	30712007	12		30428961909571209589793	23	74.688	1.000	4.399	2.000	4.697%
2021-12-05T11:01:40	mognuts	Manual testing	600000	18000000		-		-	-	0.586	-	-	3.980%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-09-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.036	-	-
1998-10-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.073	-	-
1998-12-21T00:00:00	Mark D	v4_computers	2¹	2⁶³		-	-	0.189	-	-
2000-08-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.423	-	-
2014-03-18T14:31:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.444	-	-
2014-12-03T21:51:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.444	-	-
2015-05-25T09:22:00	VictordeHollander	Manual testing	2⁶⁵	2⁶⁶		-	-	0.887	-	-
2016-01-06T20:19:36	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.774	-	-
2018-03-04T07:15:10	monst	Manual testing	2⁶⁷	2⁶⁸		-	-	3.548	-	-
2020-01-10T12:42:40	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	7.097	-	-
2021-08-19T15:51:53	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	14.19	-	-
2021-08-26T16:04:05	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	28.39	-	-
2021-10-05T16:25:55	SRBase	Manual testing	2⁷¹	2⁷²		-	-	56.77	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.191 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	1.191

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-06-19T13:27:00	Lukasz Wrobel	w1	50000	5000000						3	1.191

date	userid	compid	res64	spent (GHz-days)
2000-08-10T00:00:00	ANONYMOUS	v4_computers	7BA4995E461E3AEB	2.200
2002-10-12T00:00:00	Team Prime Rib	v4_computers	7BA4995E461E3AEB	2.200

date

userid

compid

res64

spent (GHz-days)

2000-08-10T00:00:00

ANONYMOUS

v4_computers

7BA4995E461E3AEB

2.200

2002-10-12T00:00:00

Team Prime Rib

v4_computers

7BA4995E461E3AEB

2.200

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 = 1023734, B2 = 30712007 (P-1 stage 2)

B1 = 600000, B2 = 18000000 (P-1 stage 2)

B1 = 1023734 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 100000, B2 = 1825000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 45000, B2 = 675000 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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