M1675951 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	17.7296	68.6567%	500000	15000000	0.0880	5.0151%	17.8176	70.2286%	1.5719%
PrimeNet	2⁵⁷	0.0115	63.1579%	7000	120000	0.0009	2.5713%	0.0124	64.1052%	0.9473%
GPU72	2⁶¹	0.1833	65.5738%	7000	90000	0.0008	1.2548%	0.1841	66.0057%	0.4320%
Difference	+6	+17.5463	+3.0829%	+493000	+14910000	+0.0872	+3.7604%	+17.6335	+4.2229%	+4.2229%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.7296

68.6567%

500000

15000000

0.0880

5.0151%

17.8176

70.2286%

1.5719%

PrimeNet

2⁵⁷

0.0115

63.1579%

7000

120000

0.0009

2.5713%

0.0124

64.1052%

0.9473%

GPU72

2⁶¹

0.1833

65.5738%

7000

90000

0.0008

1.2548%

0.1841

66.0057%

0.4320%

Difference

+17.5463

+3.0829%

+493000

+14910000

+0.0872

+3.7604%

+17.6335

+4.2229%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1675951	243370586518127	15	47.790	72606713 72606713	-	1	72606713	1.945e-5	0.2699	0.5042
1675951	76254403723238328097	20	66.047	22749592238448 2⁴ × 3 × 17 × 151 × 184631803	2019-03-24	151	184631803	10.294	0.6865	1.2821
1675951	430556281303059013787903	24	78.511	128451333393118001 7 × 3208013 × 5720111011	2020-01-20	3208013	5720111011	47,761	21.474	39.721

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1675951

243370586518127

47.790

72606713
72606713

72606713

1.945e-5

0.2699

0.5042

1675951

76254403723238328097

66.047

22749592238448
2⁴ × 3 × 17 × 151 × 184631803

2019-03-24

151

184631803

10.294

0.6865

1.2821

1675951

430556281303059013787903

78.511

128451333393118001
7 × 3208013 × 5720111011

2020-01-20

3208013

5720111011

47,761

21.474

39.721

exponent	prime factors	composite factor	digits	bits*
1675951	243370586518127 76254403723238328097	18558078958714559164537460063914319	35	113.838
1675951	243370586518127 430556281303059013787903	104784734709789150140854090458042817681	39	126.301
1675951	76254403723238328097 430556281303059013787903	32831812500059632211451333590597636683610591	44	144.558
1675951	243370586518127 76254403723238328097 430556281303059013787903	79902974645926862414637840252478760492009878294454 30683057	58	192.348

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:18:15	alpertron	Manual testing	500000	15000000	12	-		-	-	0.088	-	-	5.015%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:18:15

alpertron

Manual testing

500000

15000000

0.088

-

-

5.015%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.075 GHz-days
Estimated T-Level:	24.536

Digits	B1	Curves	Complete	FacMiss
20	11000	254 / 100	2.540	7.786%
25	50000	254 / 280	0.907	40.302%

New Calculation Method

Total ECM effort:	15.075 GHz-days
Estimated T-Level:	24.536

Digits	B1	Complete	FacMiss
20	11000	8.194	0.028%
25	50000	0.741	47.686%
30	250000	0.046	95.542%
35	1000000	0.002	99.791%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	4.451
50000	5000000	76254403723238328097	1	0.059
50000	5000000	430556281303059013787903	178	10.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-09-21T09:47:00	Richard B. Woods	Puttputt	50000	5000000						1	0.059
2018-02-08T21:48:51	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2019-03-24T18:15:48	Chang Chia-Tche	exbpc13	50000	5000000	76254403723238328097	66.047	1	2		1	0.059
2020-01-20T07:29:43	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.178
2020-01-20T12:09:18	TJAOI	Manual testing	50000	5000000	430556281303059013787903	78.511	178	2		178	10.56
2020-01-20T12:09:18	TJAOI	Manual testing	50000	5000000						68	4.036

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:23:25

alpertron

Manual testing

243370586518127

B6DA6BDAF6D975__

2017-10-18T13:11:57

Oliver Kruse

GTX-2

243370586518127

B6DA6BDAF6D975__

2019-03-25T16:20:23

EthanD

LexxBuntu

243370586518127

76254403723238328097

7F2CB62CCED3F97F

2019-03-26T13:24:00

kkmrkkblmbrbk

c5.large

243370586518127

76254403723238328097

7F2CB62CCED3F97F

2020-01-23T13:18:32

Jinyuan Wang

Manual testing

243370586518127

76254403723238328097

430556281303059013787903

7F2CB62CCED3F97F

2020-01-23T21:14:47

Luigi Morelli

9800X

243370586518127

76254403723238328097

430556281303059013787903

7F2CB62CCED3F97F

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

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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