M8134573 Mersenne number exponent details

Residue

Status

L-L

B1A68098B5955163

double-checked

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	2⁷²	117.5641	68.0556%	1500000	800578350	17.0511	7.9749%	134.6152	70.6031%	2.5476%
PrimeNet	2⁶³	0.1962	63.4921%	36000	900000	0.0315	3.6153%	0.2277	64.8119%	1.3199%
GPU72	2⁶⁷	3.6528	65.6716%	55000	1300000	0.0465	2.6231%	3.6993	66.5721%	0.9005%
Difference	+5	+113.9113	+2.3839%	+1445000	+799278350	+17.0046	+5.3518%	+130.9159	+4.0310%	+4.0310%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

117.5641

68.0556%

1500000

800578350

17.0511

7.9749%

134.6152

70.6031%

2.5476%

PrimeNet

2⁶³

0.1962

63.4921%

36000

900000

0.0315

3.6153%

0.2277

64.8119%

1.3199%

GPU72

2⁶⁷

3.6528

65.6716%

55000

1300000

0.0465

2.6231%

3.6993

66.5721%

0.9005%

Difference

+113.9113

+2.3839%

+1445000

+799278350

+17.0046

+5.3518%

+130.9159

+4.0310%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-03T00:00:00	Team Prime Rib	v4_computers	45000	731250		-		-	-	0.031	-	-	1.117%
2012-10-21T20:41:00	Nesowa	EPC	100000	1975000		-		-	-	0.077	-	-	1.787%
2021-12-17T14:31:11	Flaukrotist	Colab_HLM2	1500000	800578350		-		-	-	17.05	-	-	7.975%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-08-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶³		-	-	0.196	-	-
2013-09-20T19:01:00	Axelsson	Manual testing	2⁶³	2⁶⁴		-	-	0.241	-	-
2014-01-02T21:19:00	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	0.459	-	-
2015-05-26T01:41:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	0.919	-	-
2015-12-01T20:25:41	snme2pm1	Manual testing	2⁶⁶	2⁶⁷		-	-	1.837	-	-
2018-07-05T05:31:10	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	3.675	-	-
2019-12-08T18:46:30	mnd9	Manual testing	2⁶⁸	2⁶⁹		-	-	7.349	-	-
2021-08-19T16:19:54	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	14.70	-	-
2021-08-27T17:18:37	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	29.40	-	-
2021-10-15T18:27:05	SRBase	Manual testing	2⁷¹	2⁷²		-	-	58.79	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.382 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	2.382 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.231	79.392%
25	50000	0.021	97.887%
30	250000	0.001	99.865%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	2.382

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2013-02-23T09:26:00	Florimond C.	arm.durga	50000	5000000						3	1.191
2019-04-27T03:58:09	10-Us	wethouderhacking	50000	5000000						3	1.191

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-05-10T00:00:00	ANONYMOUS	v4_computers	B1A68098B5955163	2.124
2002-08-03T00:00:00	Team Prime Rib	v4_computers	B1A68098B5955163	2.124

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 = 1500000, B2 = 800578350 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 100000, B2 = 1975000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 45000, B2 = 731250 (P-1 stage 2)

B1 = 45000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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