M3146657 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	18.9423	67.6471%	1000000	119912100	0.9229	7.4934%	19.8652	70.0714%	2.4243%
PrimeNet	2⁶⁰	0.0488	63.3333%	13000	240000	0.0031	2.6493%	0.0519	64.3048%	0.9714%
GPU72	2⁶⁴	1.1311	65.6250%	15000	240000	0.0034	1.5439%	1.1345	66.1557%	0.5307%
Difference	+4	+17.8111	+2.0221%	+985000	+119672100	+0.9196	+5.9495%	+18.7307	+3.9157%	+3.9157%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

18.9423

67.6471%

1000000

119912100

0.9229

7.4934%

19.8652

70.0714%

2.4243%

PrimeNet

2⁶⁰

0.0488

63.3333%

13000

240000

0.0031

2.6493%

0.0519

64.3048%

0.9714%

GPU72

2⁶⁴

1.1311

65.6250%

15000

240000

0.0034

1.5439%

1.1345

66.1557%

0.5307%

Difference

+17.8111

+2.0221%

+985000

+119672100

+0.9196

+5.9495%

+18.7307

+3.9157%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3146657	1661434897	10	30.630	264 2³ × 3 × 11	-	8	11	4.806e-11	1.007e-6	2.009e-6
3146657	2893229946325559	16	51.362	459730747 7 × 65675821	2014-06-25	7	65675821	0.0002	0.4416	0.8248

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3146657

1661434897

30.630

264
2³ × 3 × 11

4.806e-11

1.007e-6

2.009e-6

3146657

2893229946325559

51.362

459730747
7 × 65675821

2014-06-25

65675821

0.0002

0.4416

0.8248

exponent	prime factors	composite factor	digits	bits*
3146657	1661434897 2893229946325559	4806913197870720645632423	25	81.991

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-17T07:54:55	Jocelyn Larouche	Manual testing	314665	3146657	6	-	skipped known factor: 1661434897	-	-	0.058	-	-	3.338%
2022-02-12T07:46:46	Jocelyn Larouche	Manual testing	1000000	119912100		-	skipped known factor: 1661434897 skipped known factor: 2893229946325559	-	-	0.923	-	-	7.493%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-06-25T11:28:00	TJAOI	Manual testing	?	?	2893229946325559	51.362	16	7.81443e-5	0.592	0.000
2021-01-17T07:54:58	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.750	-	-
2021-09-21T11:06:30	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.499	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.351 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:	0.351 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	0.351

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-08-09T12:09:23	Oliver Kruse	ECM-HTC	50000	5000000						3	0.351

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-30T20:12:13

Oliver Kruse

GTX-0

1661434897

2893229946325559

E4F73271B79FE5__

2017-12-12T12:28:29

kkmrkkblmbrbk

c4.xlarge

1661434897

2893229946325559

E4F73271B79FE5__

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 = 119912100 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 314665, B2 = 3146657 (P-1 stage 2)

B1 = 314665 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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