M8 101 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
Actual	unknown	100000000	100000000	0.0147	26.2010%	0.0147	26.2010%
Target	2⁴⁴	0.0003	70.4545%	500	10000	0.0000	1.1844%	0.0003	70.8045%
Difference	-44	-0.0003	-70.4545%	+99999500	+99990000	+0.0147	+25.0167%	+0.0145	-44.6035%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

unknown

100000000

0.0147

26.2010%

0.0147

26.2010%

Target

2⁴⁴

0.0003

70.4545%

500

10000

0.0000

1.1844%

0.0003

70.8045%

Difference

-44

-0.0003

-70.4545%

+99999500

+99990000

+0.0147

+25.0167%

+0.0145

-44.6035%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8101	712889	6	19.443	44 2² × 11	-	4	11	8.704e-12	6.459e-10	1.200e-9
8101	11072206468574816189936903	26	83.195	683385166558129625351 47 × 83 × 3967 × 313981 × 140644913	-	313981	140644913	430,815,930	0.0012	0.0021

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

8101

712889

19.443

44
2² × 11

8.704e-12

6.459e-10

1.200e-9

8101

11072206468574816189936903

83.195

683385166558129625351
47 × 83 × 3967 × 313981 × 140644913

313981

140644913

430,815,930

0.0012

0.0021

exponent	prime factors	composite factor	digits	bits*
8101	712889 11072206468574816189936903	7893254197175832138827928842767	31	102.638

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-12-16	Lisander Viaene	Desktop	100000000	100000000		-	skipped known factor: 712889	-	-	0.015	-	-	26.201%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-12-16

Lisander Viaene

Desktop

100000000

skipped known factor: 712889

0.015

-

-

26.201%

ECM factoring results:

Total ECM effort:	1,299.498 GHz-days
Estimated T-Level:	44.256

Digits	B1	Complete	FacMiss
20	11000	2,434.800	0.000%
25	50000	677.955	0.000%
30	250000	173.305	0.000%
35	1000000	34.550	0.000%
40	3000000	5.808	0.300%
45	11000000	0.851	42.690%
50	44000000	0.110	89.583%
55	110000000	0.013	98.726%
60	260000000	0.001	99.872%

ECM Summary

B1	B2	curves	GHz-days
3000000	300000000	3,924	24.97
11000000	36578884662	2,400	643.5
11000000	99324315090	900	631.0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.006
2013-04-18	Axon		3000000	300000000						30	0.191
2016-12-20	James Hintz	alek_07_13_2016	3000000	300000000						100	0.636
2017-05-17	kkmrkkblmbrbk	old	3000000	300000000						3793	24.14
2020-12-17	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-28	Denial140	i5-8400	11000000	99324315090						150	105.2

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

712889

11072206468574816189936903

849C3AFA238F04__

2017-09-21

Oliver Kruse

Manual testing

712889

11072206468574816189936903

849C3AFA238F04__

2017-10-12

kkmrkkblmbrbk

Manual testing

712889

11072206468574816189936903

849C3AFA238F04__

2020-04-17

Oliver Kruse

Manual testing

712889

11072206468574816189936903

56F6DCA88EA54F__

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 = 100000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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