M1951051 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	15.2297	68.6567%	500000	15000000	0.1015	5.1078%	15.3312	70.2577%	1.6010%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4670%	0.0209	64.6863%	0.8932%
GPU72	2⁶²	0.3149	66.1290%	8000	90000	0.0010	1.1532%	0.3159	66.5196%	0.3906%
Difference	+5	+14.9148	+2.5277%	+492000	+14910000	+0.1005	+3.9546%	+15.0153	+3.7380%	+3.7380%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2297

68.6567%

500000

15000000

0.1015

5.1078%

15.3312

70.2577%

1.6010%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4670%

0.0209

64.6863%

0.8932%

GPU72

2⁶²

0.3149

66.1290%

8000

90000

0.0010

1.1532%

0.3159

66.5196%

0.3906%

Difference

+14.9148

+2.5277%

+492000

+14910000

+0.1005

+3.9546%

+15.0153

+3.7380%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1951051	81944143	8	26.288	21 3 × 7	-	3	7	4.603e-12	2.531e-7	4.803e-7
1951051	242759676940297518983	21	67.718	62212540046441 62212540046441	2020-11-22	1	62212540046441	30.089	266,627	497,986

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1951051

81944143

26.288

21
3 × 7

4.603e-12

2.531e-7

4.803e-7

1951051

242759676940297518983

67.718

62212540046441
62212540046441

2020-11-22

62212540046441

30.089

266,627

497,986

exponent	prime factors	composite factor	digits	bits*
1951051	81944143 242759676940297518983	19892733681829542358088166569	29	94.006

exponent

prime factors

composite factor

digits

bits*

1951051

81944143
242759676940297518983

19892733681829542358088166569

94.006

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:13	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 81944143	-	-	0.101	-	-	5.108%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:13

alpertron

Manual testing

500000

15000000

skipped known factor: 81944143

0.101

-

-

5.108%

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.973 GHz-days
Estimated T-Level:	24.571

Digits	B1	Curves	Complete	FacMiss
20	11000	256 / 100	2.560	7.631%
25	50000	256 / 280	0.914	40.015%

New Calculation Method

Total ECM effort:	20.973 GHz-days
Estimated T-Level:	24.571

Digits	B1	Complete	FacMiss
20	11000	9.040	0.012%
25	50000	0.803	44.792%
30	250000	0.050	95.142%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		11	0.765
50000	5000000	242759676940297518983	4	0.278
50000	5524853		14	1.015
50000	6750000		14	1.111
50000	7500000		213	17.80

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-07-26T08:52:24	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-14T14:15:36	Oliver Kruse	ECM-HTC	50000	5000000						3	0.209
2020-11-22T18:17:24	MarkS	desktop-i7	50000	5000000	242759676940297518983	67.718	4	2	8839796768131770	4	0.278
2021-01-20T10:46:58	seatsea	dt	50000	5524853						7	0.508
2021-04-25T21:09:37	nordi	sweet16	50000	6750000						7	0.556
2021-07-14T09:01:52	seatsea	Manual testing	50000	5524853						7	0.508
2021-11-07T16:19:41	Dylan Delgado	colab	50000	6750000						7	0.556
2022-04-05T21:34:56	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-04-21T11:52:21	TJAOI	Manual testing	50000	7500000						213	17.80

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T05:34:24

Oliver Kruse

GTX-0

81944143

B510D78D331295__

2017-11-11T13:04:12

kkmrkkblmbrbk

c4.xlarge

81944143

B510D78D331295__

2020-11-23T17:23:06

rbanov

ccg_lnx01

81944143

242759676940297518983

EC14D7FD79696088

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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