M3468281 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	17.1857	67.6471%	1305589	111642300	1.1143	7.7033%	18.3000	70.1393%	2.4923%
PrimeNet	2⁶⁰	0.0443	63.3333%	15000	280000	0.0045	2.9041%	0.0488	64.3982%	1.0648%
GPU72	2⁶⁴	1.0263	65.6250%	19000	360000	0.0057	1.8856%	1.0320	66.2732%	0.6482%
Difference	+4	+16.1595	+2.0221%	+1286589	+111282300	+1.1086	+5.8177%	+17.2681	+3.8661%	+3.8661%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.1857

67.6471%

1305589

111642300

1.1143

7.7033%

18.3000

70.1393%

2.4923%

PrimeNet

2⁶⁰

0.0443

63.3333%

15000

280000

0.0045

2.9041%

0.0488

64.3982%

1.0648%

GPU72

2⁶⁴

1.0263

65.6250%

19000

360000

0.0057

1.8856%

1.0320

66.2732%

0.6482%

Difference

+16.1595

+2.0221%

+1286589

+111282300

+1.1086

+5.8177%

+17.2681

+3.8661%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3468281	113953840537	12	36.730	16428 2² × 3 × 37²	-	1369	1369	4.107e-9	0.0002	0.0004

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3468281

113953840537

36.730

16428
2² × 3 × 37²

1369

4.107e-9

0.0002

0.0004

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-18T10:49:30	Jocelyn Larouche	Manual testing	346828	3468281	6	-	skipped known factor: 113953840537	-	-	0.079	-	-	3.501%
2022-01-06T11:34:46	Jocelyn Larouche	Manual testing	1305589	111642300		-	skipped known factor: 113953840537	-	-	1.114	-	-	7.703%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-02-28T12:18:16	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.155	-	-
2022-05-20T15:54:44	gLauss	Manual testing	2⁶⁶	2⁶⁷		-	-	4.309	-	-
2022-05-20T00:17:29	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.309	-	-
2021-06-02T11:00:40	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.618	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.441 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:	0.441 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	0.441

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-03T02:59:49	rucio		50000	5000000						3	0.441

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-06T18:00:59

kkmrkkblmbrbk

c4.xlarge

113953840537

7B56F3B05870C5__

2017-11-23T02:02:09

Oliver Kruse

Threadripper

113953840537

7B56F3B05870C5__

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 = 1305589, B2 = 111642300 (P-1 stage 2)

B1 = 1305589 (P-1 stage 1)

B1 = 346828, B2 = 3468281 (P-1 stage 2)

B1 = 346828 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

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