M3512603 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	2⁶⁸	16.9689	67.6471%	1000000	145208700	1.3488	7.7910%	18.3177	70.1677%	2.5206%
PrimeNet	2⁶⁰	0.0437	63.3333%	15000	300000	0.0046	2.9623%	0.0484	64.4195%	1.0862%
GPU72	2⁶⁴	1.0133	65.6250%	20000	360000	0.0059	1.9167%	1.0192	66.2839%	0.6589%
Difference	+4	+15.9556	+2.0221%	+980000	+144848700	+1.3430	+5.8743%	+17.2985	+3.8838%	+3.8838%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

16.9689

67.6471%

1000000

145208700

1.3488

7.7910%

18.3177

70.1677%

2.5206%

PrimeNet

2⁶⁰

0.0437

63.3333%

15000

300000

0.0046

2.9623%

0.0484

64.4195%

1.0862%

GPU72

2⁶⁴

1.0133

65.6250%

20000

360000

0.0059

1.9167%

1.0192

66.2839%

0.6589%

Difference

+15.9556

+2.0221%

+980000

+144848700

+1.3430

+5.8743%

+17.2985

+3.8838%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3512603	6835054749199	13	42.636	972933 3 × 13² × 19 × 101	-	169	169	2.655e-7	2.574e-5	5.238e-5
3512603	249420266746808499049	21	67.757	35503623202908 2² × 3 × 7 × 67 × 107 × 769 × 76667	2018-11-04	769	76667	8.7687	0.0007	0.0012

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3512603

6835054749199

42.636

972933
3 × 13² × 19 × 101

169

2.655e-7

2.574e-5

5.238e-5

3512603

249420266746808499049

67.757

35503623202908
2² × 3 × 7 × 67 × 107 × 769 × 76667

2018-11-04

769

76667

8.7687

0.0007

0.0012

exponent	prime factors	composite factor	digits	bits*
3512603	6835054749199 249420266746808499049	1704801178774254845101044325011751	34	110.393

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-10-12T02:46:38	Jocelyn Larouche	Manual testing	351260	3512603	6	-	skipped known factor: 6835054749199 skipped known factor: 249420266746808499049	-	-	0.080	-	-	3.522%
2022-04-25T11:28:05	Jocelyn Larouche	Manual testing	1000000	145208700		-	skipped known factor: 6835054749199 skipped known factor: 249420266746808499049	-	-	1.349	-	-	7.791%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-02-08T17:28:38	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	249420266746808499049	67.757	21	0.309	0.749	0.629

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.148 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.148 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	249420266746808499049	1	0.148

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-04T13:37:24	ATH	ec2-ECMCF	50000	5000000	249420266746808499049	67.757	1	2		1	0.148

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T15:59:18

kkmrkkblmbrbk

c4.xlarge

6835054749199

80BFB8525C1D1B__

2017-11-24T11:57:29

Oliver Kruse

GTX-2

6835054749199

80BFB8525C1D1B__

2018-11-07T08:55:58

Luigi Morelli

GoogleCloudTmp

6835054749199

249420266746808499049

80BFB8525C1D1B__

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 = 1000000, B2 = 145208700 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 351260, B2 = 3512603 (P-1 stage 2)

B1 = 351260 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

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