M3698531 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	16.1158	67.6471%	1000000	147585900	1.3685	7.8511%	17.4844	70.1871%	2.5401%
PrimeNet	2⁶⁰	0.0415	63.3333%	16000	320000	0.0050	3.0834%	0.0465	64.4639%	1.1306%
GPU72	2⁶⁴	0.9624	65.6250%	22000	450000	0.0069	2.1055%	0.9693	66.3488%	0.7238%
Difference	+4	+15.1535	+2.0221%	+978000	+147135900	+1.3616	+5.7456%	+16.5151	+3.8384%	+3.8384%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

16.1158

67.6471%

1000000

147585900

1.3685

7.8511%

17.4844

70.1871%

2.5401%

PrimeNet

2⁶⁰

0.0415

63.3333%

16000

320000

0.0050

3.0834%

0.0465

64.4639%

1.1306%

GPU72

2⁶⁴

0.9624

65.6250%

22000

450000

0.0069

2.1055%

0.9693

66.3488%

0.7238%

Difference

+15.1535

+2.0221%

+978000

+147135900

+1.3616

+5.7456%

+16.5151

+3.8384%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3698531	7397063	7	22.819	1 1	-	1	1	1.511e-13	1.523e-7	3.099e-7

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3698531

7397063

22.819

1
1

1.511e-13

1.523e-7

3.099e-7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-11-04T12:41:34	Jocelyn Larouche	Manual testing	400000	7397062	6	-	skipped known factor: 7397063	-	-	0.119	-	-	4.244%
2022-04-05T14:54:03	Jocelyn Larouche	Manual testing	1000000	147585900		-	skipped known factor: 7397063	-	-	1.369	-	-	7.851%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-02-11T23:31:30	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.082	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.447 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:	0.447 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	0.447

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-12T15:31:09	rucio		50000	5000000						3	0.447

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T19:21:30

kkmrkkblmbrbk

Manual testing

7397063

97E31B1D9DEF89__

2017-11-30T08:21:17

Oliver Kruse

Threadripper

7397063

97E31B1D9DEF89__

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 = 147585900 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 400000, B2 = 7397062 (P-1 stage 2)

B1 = 400000 (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

2²⁰

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