M112 866 001 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

5C649FEC235E12DD

PRP-tested

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁷	271.1903	64.9351%	4500000	135000000	73.8848	6.0087%	345.0751	67.0420%
Target	2⁷⁶	135.5944	64.4737%	700000	26000000	13.2268	4.0604%	148.8212	65.9162%
Difference	+1	+135.5959	+0.4614%	+3800000	+109000000	+60.6580	+1.9483%	+196.2539	+1.1258%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁷

271.1903

64.9351%

4500000

135000000

73.8848

6.0087%

345.0751

67.0420%

Target

2⁷⁶

135.5944

64.4737%

700000

26000000

13.2268

4.0604%

148.8212

65.9162%

Difference

+135.5959

+0.4614%

+3800000

+109000000

+60.6580

+1.9483%

+196.2539

+1.1258%

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-11-23	Ernst W. Mayer	Manual testing	4500000	135000000		-		-	-	73.88	-	-	6.009%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-11-23

Ernst W. Mayer

Manual testing

4500000

135000000

73.88

-

-

6.009%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2010-05-05	Martti Järvi	Tiny	2⁶³	2⁶⁴		-	-	0.017	-	-
2010-09-28	Nathan Edington	Maryland	2⁶⁴	2⁶⁵		-	-	0.033	-	-
2012-06-03	Donna Noble	Opt6128x4x4	2⁶⁵	2⁶⁶		-	-	0.066	-	-
2014-11-11	poweredge	poweredge	2⁶⁶	2⁶⁷		-	-	0.132	-	-
2015-02-07	C.D.B.	i7-2600K_4500MHz	2⁶⁷	2⁶⁸		-	-	0.265	-	-
2015-02-08	C.D.B.	i7-2600K_4500MHz	2⁶⁸	2⁶⁹		-	-	0.530	-	-
2015-02-11	C.D.B.	i7-2600K_4500MHz	2⁶⁹	2⁷⁰		-	-	1.059	-	-
2015-02-12	C.D.B.	i7-2600K_4500MHz	2⁷⁰	2⁷¹		-	-	2.119	-	-
2019-01-08	Niels_Mache_Nextcloud	Manual testing	2⁷¹	2⁷²		-	-	4.237	-	-
2020-04-04	tsc	Manual testing	2⁷²	2⁷³		-	-	8.475	-	-
2020-07-26	tsc	Manual testing	2⁷³	2⁷⁴		-	-	16.95	-	-
2020-11-25	arpcar	Manual testing	2⁷⁴	2⁷⁵		-	-	33.90	-	-
2020-12-01	arpcar	Manual testing	2⁷⁵	2⁷⁶		-	-	67.80	-	-
2020-12-16	arpcar	Manual testing	2⁷⁶	2⁷⁷		-	-	135.6	-	-

date	userid	compid	cofactors	res64	PRP
2021-11-25	Ernst W. Mayer	Manual testing		5C649FEC235E12DD	no

date

userid

compid

cofactors

res64

PRP

2021-11-25

Ernst W. Mayer

Manual testing

5C649FEC235E12DD

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 = 4500000, B2 = 135000000 (P-1 stage 2)

B1 = 4500000 (P-1 stage 1)

10⁵

10⁶

10⁷

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁷⁷

2⁷⁶

2⁷⁵

2⁷⁴

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 76

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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