M3410881 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	17.4749	67.6471%	1000000	114656850	1.0953	7.5089%	18.5702	70.0764%	2.4294%
PrimeNet	2⁶⁰	0.0450	63.3333%	14000	280000	0.0043	2.8488%	0.0494	64.3779%	1.0446%
GPU72	2⁶⁴	1.0435	65.6250%	19000	320000	0.0054	1.8203%	1.0489	66.2507%	0.6257%
Difference	+4	+16.4314	+2.0221%	+981000	+114336850	+1.0899	+5.6887%	+17.5213	+3.8257%	+3.8257%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

17.4749

67.6471%

1000000

114656850

1.0953

7.5089%

18.5702

70.0764%

2.4294%

PrimeNet

2⁶⁰

0.0450

63.3333%

14000

280000

0.0043

2.8488%

0.0494

64.3779%

1.0446%

GPU72

2⁶⁴

1.0435

65.6250%

19000

320000

0.0054

1.8203%

1.0489

66.2507%

0.6257%

Difference

+16.4314

+2.0221%

+981000

+114336850

+1.0899

+5.6887%

+17.5213

+3.8257%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3410881	327444577	9	28.287	48 2⁴ × 3	-	16	16	1.059e-11	2.437e-6	4.959e-6
3410881	5590857991318227948479	22	72.244	819562158767519 79 × 874711 × 11860151	2018-10-31	874711	11860151	458.77	0.2244	0.2711

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3410881

327444577

28.287

48
2⁴ × 3

1.059e-11

2.437e-6

4.959e-6

3410881

5590857991318227948479

72.244

819562158767519
79 × 874711 × 11860151

2018-10-31

874711

11860151

458.77

0.2244

0.2711

exponent	prime factors	composite factor	digits	bits*
3410881	327444577 5590857991318227948479	1830696130034266822979283948383	31	100.530

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-02-18T21:10:22	Jocelyn Larouche	Manual testing	341088	3751969	6	-	skipped known factor: 327444577	-	-	0.080	-	-	3.551%
2021-03-16T01:10:03	Jocelyn Larouche	Manual testing	341088	7162850	6	-	skipped known factor: 327444577	-	-	0.109	-	-	4.090%
2022-01-24T14:48:14	Jocelyn Larouche	Manual testing	1000000	114656850		-	skipped known factor: 327444577 skipped known factor: 5590857991318227948479	-	-	1.095	-	-	7.509%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-10-10T20:46:08	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.763	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.440 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:	0.440 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	5590857991318227948479	3	0.440

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-31T05:41:43	MarkS	laptop64	50000	5000000	5590857991318227948479	72.244	3	2		3	0.440

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-05T19:53:21

kkmrkkblmbrbk

c4.xlarge

327444577

92B2242A258336__

2017-11-21T10:18:07

Oliver Kruse

GTX-3

327444577

92B2242A258336__

2018-10-31T06:22:41

rucio

327444577

5590857991318227948479

92B2242A258336__

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 = 114656850 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 341088, B2 = 7162850 (P-1 stage 2)

B1 = 341088, B2 = 3751969 (P-1 stage 2)

B1 = 341088 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

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