M3881093 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	15.3578	67.6471%	500000	130364850	1.3700	7.1342%	16.7277	69.9552%	2.3081%
PrimeNet	2⁶⁰	0.0396	63.3333%	17000	360000	0.0065	3.2450%	0.0460	64.5232%	1.1898%
GPU72	2⁶⁴	0.9171	65.6250%	24000	500000	0.0090	2.2314%	0.9261	66.3921%	0.7671%
Difference	+4	+14.4407	+2.0221%	+476000	+129864850	+1.3610	+4.9027%	+15.8016	+3.5631%	+3.5631%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

15.3578

67.6471%

500000

130364850

1.3700

7.1342%

16.7277

69.9552%

2.3081%

PrimeNet

2⁶⁰

0.0396

63.3333%

17000

360000

0.0065

3.2450%

0.0460

64.5232%

1.1898%

GPU72

2⁶⁴

0.9171

65.6250%

24000

500000

0.0090

2.2314%

0.9261

66.3921%

0.7671%

Difference

+14.4407

+2.0221%

+476000

+129864850

+1.3610

+4.9027%

+15.8016

+3.5631%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3881093	19883887334111	14	44.177	2561635 5 × 541 × 947	-	541	947	8.855e-7	0.0001	0.0002
3881093	973375876003774997777	21	69.722	125399710339816 2³ × 11 × 751 × 787 × 2411011	2018-11-20	787	2411011	56.874	0.0239	0.0444

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3881093

19883887334111

44.177

2561635
5 × 541 × 947

541

947

8.855e-7

0.0001

0.0002

3881093

973375876003774997777

69.722

125399710339816
2³ × 11 × 751 × 787 × 2411011

2018-11-20

787

2411011

56.874

0.0239

0.0444

exponent	prime factors	composite factor	digits	bits*
3881093	19883887334111 973375876003774997777	19354496252200660936720387481271247	35	113.898

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-04-17T22:55:05	Jocelyn Larouche	Manual testing	200000	200000		-	skipped known factor: 19883887334111	-	-	0.036	-	-	1.299%
2022-05-16T19:05:00	Jocelyn Larouche	Manual testing	500000	130364850		-	skipped known factor: 19883887334111 skipped known factor: 973375876003774997777	-	-	1.370	-	-	7.134%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2022-03-16T19:11:58	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	7.702	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.536 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:	0.536 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	973375876003774997777	3	0.536

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-20T19:12:49	ATH	ec2-ECMCF	50000	5000000	973375876003774997777	69.722	3	2		3	0.536

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T16:57:29

kkmrkkblmbrbk

Manual testing

19883887334111

2AF0901CD2F99E__

2017-12-26T22:34:29

Oliver Kruse

GTX-4

19883887334111

2AF0901CD2F99E__

2018-11-20T19:46:13

rucio

19883887334111

973375876003774997777

15EEA640B459E6__

2018-11-21T12:02:23

kkmrkkblmbrbk

c5d.large

19883887334111

973375876003774997777

15EEA640B459E6__

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 = 500000, B2 = 130364850 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000 (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