M1931309 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	15.3854	68.6567%	500000	15000000	0.1015	5.1016%	15.4869	70.2557%	1.5990%
PrimeNet	2⁵⁸	0.0199	63.7931%	8000	140000	0.0012	2.4622%	0.0211	64.6846%	0.8915%
GPU72	2⁶²	0.3181	66.1290%	8000	90000	0.0010	1.1507%	0.3191	66.5188%	0.3898%
Difference	+5	+15.0673	+2.5277%	+492000	+14910000	+0.1005	+3.9508%	+15.1678	+3.7369%	+3.7369%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3854

68.6567%

500000

15000000

0.1015

5.1016%

15.4869

70.2557%

1.5990%

PrimeNet

2⁵⁸

0.0199

63.7931%

8000

140000

0.0012

2.4622%

0.0211

64.6846%

0.8915%

GPU72

2⁶²

0.3181

66.1290%

8000

90000

0.0010

1.1507%

0.3191

66.5188%

0.3898%

Difference

+15.0673

+2.5277%

+492000

+14910000

+0.1005

+3.9508%

+15.1678

+3.7369%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1931309	15450473	8	23.881	4 2²	-	4	4	5.791e-13	3.146e-7	6.404e-7
1931309	74126775865817	14	46.075	19190812 2² × 59 × 233 × 349	2014-02-04	233	349	9.006e-6	1.883e-5	3.730e-5
1931309	206872507641370128839153	24	77.453	53557589086306264 2³ × 61458679 × 108930077	2020-11-06	61458679	108930077	27,594	5.0379	9.839

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1931309

15450473

23.881

4
2²

5.791e-13

3.146e-7

6.404e-7

1931309

74126775865817

46.075

19190812
2² × 59 × 233 × 349

2014-02-04

233

349

9.006e-6

1.883e-5

3.730e-5

1931309

206872507641370128839153

77.453

53557589086306264
2³ × 61458679 × 108930077

2020-11-06

61458679

108930077

27,594

5.0379

9.839

exponent	prime factors	composite factor	digits	bits*
1931309	15450473 74126775865817	1145293749091857181441	22	69.956
1931309	15450473 206872507641370128839153	3196278093755282858635854769369	31	101.334
1931309	74126775865817 206872507641370128839153	15334792006731358180709066462703933001	38	123.528
1931309	15450473 74126775865817 206872507641370128839153	236929789860618667824374552237212623825759473	45	147.409

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:42	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 15450473 skipped known factor: 74126775865817	-	-	0.101	-	-	5.102%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-02-04T11:43:00	TJAOI	Manual testing	?	?	74126775865817	46.075	14	4.15209e-6	0.233	9.21562e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-02-04T11:43:00

TJAOI

Manual testing

74126775865817

46.075

4.15209e-6

0.233

9.21562e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.422 GHz-days
Estimated T-Level:	24.446

Digits	B1	Curves	Complete	FacMiss
20	11000	249 / 100	2.490	8.188%
25	50000	249 / 280	0.889	41.030%

New Calculation Method

Total ECM effort:	19.422 GHz-days
Estimated T-Level:	24.446

Digits	B1	Complete	FacMiss
20	11000	8.546	0.019%
25	50000	0.774	46.131%
30	250000	0.048	95.325%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	0.417
50000	5000000	206872507641370128839153	5	0.347
50000	6338636		14	1.078
50000	6600000		210	16.47
50000	6750000		14	1.110

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-20T10:46:28	Gordon Spence	haswell	50000	5000000						3	0.208
2019-02-10T06:58:25	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-11-06T18:22:30	nordi	sweet16	50000	5000000	206872507641370128839153	77.453	5	2	2544677737032957	5	0.347
2021-01-20T11:16:24	seatsea	dt	50000	6338636						7	0.539
2021-04-27T11:49:42	nordi	sweet16	50000	6750000						7	0.555
2021-07-14T09:01:53	seatsea	Manual testing	50000	6338636						7	0.539
2021-11-16T16:01:29	LordJulius	surface7	50000	6750000						7	0.555
2022-03-03T12:28:40	TJAOI	Manual testing	50000	6600000						210	16.47

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T01:10:34

Oliver Kruse

GTX-3

15450473

74126775865817

E115C163CB9094__

2017-11-10T16:33:17

kkmrkkblmbrbk

c4.xlarge

15450473

74126775865817

E115C163CB9094__

2020-11-07T11:51:22

mrh

15450473

74126775865817

206872507641370128839153

6B434637896351D9

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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