M18800567 Mersenne number exponent details

Residue

Status

L-L

1E9924835E57739E

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	2⁷³	101.7440	65.7534%	1000000	181212780	10.0003	6.2437%	111.7443	67.8917%	2.1382%
PrimeNet	2⁶⁵	0.3881	61.5385%	90000	2800000	0.2197	4.8255%	0.6077	63.3944%	1.8560%
GPU72	2⁶⁹	6.3502	63.7681%	130000	3600000	0.2949	3.4748%	6.6451	65.0271%	1.2590%
Difference	+4	+95.3938	+1.9853%	+870000	+177612780	+9.7054	+2.7689%	+105.0992	+2.8646%	+2.8646%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷³

101.7440

65.7534%

1000000

181212780

10.0003

6.2437%

111.7443

67.8917%

2.1382%

PrimeNet

2⁶⁵

0.3881

61.5385%

90000

2800000

0.2197

4.8255%

0.6077

63.3944%

1.8560%

GPU72

2⁶⁹

6.3502

63.7681%

130000

3600000

0.2949

3.4748%

6.6451

65.0271%

1.2590%

Difference

+95.3938

+1.9853%

+870000

+177612780

+9.7054

+2.7689%

+105.0992

+2.8646%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
18800567	25994442631285580459191	23	74.461	691320709404285 3 × 5 × 17 × 2711061605507	2022-04-08	17	2711061605507	218.69	136,536	255,011

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

18800567

25994442631285580459191

74.461

691320709404285
3 × 5 × 17 × 2711061605507

2022-04-08

2711061605507

218.69

136,536

255,011

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-04-10T00:00:00	ANONYMOUS	v4_computers	225000	5512500		-		-	-	0.474	-	-	2.694%
2003-08-25T00:00:00	ANONYMOUS	v4_computers	225000	5512500		-		-	-	0.474	-	-	2.694%
2022-03-26T02:14:53	masser	Manual testing	1000000	181212780		-		-	-	10.00	-	-	6.244%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-04-08T03:19:25	masser	Manual testing	200000	4200000	6	5	25994442631285580459191	P+1	23	74.461	0.457
2022-04-11T03:41:11	masser	Manual testing	50000	700000	135	71			-	-	0.098

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-20T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-12-08T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.004	-	-
2002-03-16T00:00:00	Team Prime Rib	v4_computers	2¹	2⁶⁶		-	-	0.786	-	-
2014-08-02T11:13:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.795	-	-
2017-09-18T11:30:16	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	1.590	-	-
2017-09-18T11:30:16	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.180	-	-
2020-01-22T12:43:06	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	6.360	-	-
2021-09-12T16:51:02	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	12.72	-	-
2021-10-08T19:10:27	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	25.44	-	-
2021-11-19T21:07:55	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	50.88	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.969 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.969 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.969

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2019-04-21T23:02:43	kracker	i5-4670K	50000	5000000						1	0.969

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-05-19T00:00:00	ANONYMOUS	v4_computers	1E9924835E57739E	11.99
2003-08-25T00:00:00	ANONYMOUS	v4_computers	1E9924835E57739E	11.99
2007-02-20T00:00:00	TheJudger	v4_computers	1E9924835E57739E	11.99

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 = 181212780 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 225000, B2 = 5512500 (P-1 stage 2)

B1 = 200000, B2 = 4200000 (P+1 stage 2)

B1 = 225000 (P-1 stage 1)

B1 = 200000 (P+1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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