M5551801 Mersenne number exponent details

Residue

Status

L-L

6381AEC59BBC1BC1

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	2⁷⁵	1,378.2750	69.3333%	2000000	112000000	1.8303	4.6334%	1,380.1052	70.7542%	1.4209%
PrimeNet	2⁶²	0.1107	62.9032%	24000	550000	0.0121	3.1662%	0.1227	64.0778%	1.1746%
GPU72	2⁶⁶	2.6601	65.1515%	34000	700000	0.0161	2.1570%	2.6762	65.9032%	0.7517%
Difference	+9	+1,375.6149	+4.1818%	+1966000	+111300000	+1.8142	+2.4764%	+1,377.4290	+4.8510%	+4.8510%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁵

1,378.2750

69.3333%

2000000

112000000

1.8303

4.6334%

1,380.1052

70.7542%

1.4209%

PrimeNet

2⁶²

0.1107

62.9032%

24000

550000

0.0121

3.1662%

0.1227

64.0778%

1.1746%

GPU72

2⁶⁶

2.6601

65.1515%

34000

700000

0.0161

2.1570%

2.6762

65.9032%

0.7517%

Difference

+1,375.6149

+4.1818%

+1966000

+111300000

+1.8142

+2.4764%

+1,377.4290

+4.8510%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-07-25T00:00:00	ANONYMOUS	v4_computers	25000	156250		-		-	-	0.007	-	-	0.326%
2010-11-25T04:04:00	Squeeky_Squirrel	P4_2600	65000	1121250		-		-	-	0.028	-	-	0.870%
2013-05-19T12:14:00	Squeeky_Squirrel	P4_2600	175000	3937500		-		-	-	0.087	-	-	1.574%
2021-10-19T13:29:41	Architects Cubed	burrow	2000000	112000000		-		-	-	1.830	-	-	4.633%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:39:10	Mark Rose	Manual testing	2¹	2⁶²		-	-	0.111	-	-
2009-04-23T19:20:00	GrunwalderGIMP	Manual testing	2⁶²	2⁶³		-	-	0.177	-	-
2012-06-27T11:26:00	dbaugh	Manual testing	2⁶³	2⁶⁴		-	-	0.354	-	-
2012-07-07T12:36:00	dbaugh	Manual testing	2⁶⁴	2⁶⁵		-	-	0.673	-	-
2012-07-11T04:38:00	dbaugh	Manual testing	2⁶⁵	2⁶⁶		-	-	1.346	-	-
2012-07-11T04:38:00	dbaugh	Manual testing	2⁶⁶	2⁶⁷		-	-	2.692	-	-
2012-08-12T07:06:00	dbaugh	Manual testing	2⁶⁷	2⁶⁸		-	-	5.384	-	-
2012-08-15T08:42:00	dbaugh	Manual testing	2⁶⁸	2⁶⁹		-	-	10.77	-	-
2012-09-29T08:21:00	dbaugh	Manual testing	2⁶⁹	2⁷⁰		-	-	21.54	-	-
2012-10-19T00:19:00	dbaugh	Manual testing	2⁷⁰	2⁷¹		-	-	43.07	-	-
2012-11-24T17:03:00	dbaugh	Manual testing	2⁷¹	2⁷²		-	-	86.14	-	-
2013-05-06T06:53:00	dbaugh	Manual testing	2⁷²	2⁷³		-	-	172.3	-	-
2013-09-09T04:53:00	dbaugh	Manual testing	2⁷³	2⁷⁴		-	-	344.6	-	-
2013-12-09T01:19:00	dbaugh	Manual testing	2⁷⁴	2⁷⁵		-	-	689.2	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.122 GHz-days
Estimated T-Level:	0.650

Digits	B1	Curves	Complete	FacMiss
20	11000	13 / 100	0.130	87.752%
25	50000	13 / 280	0.046	95.455%

New Calculation Method

Total ECM effort:	3.122 GHz-days
Estimated T-Level:	0.650

Digits	B1	Complete	FacMiss
20	11000	0.419	65.747%
25	50000	0.038	96.281%
30	250000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		13	3.122

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-01-31T18:23:00	S00030	op9020-usff	50000	5000000						3	0.720
2012-10-11T11:58:00	dbaugh	Manual testing	50000	5000000						10	2.401

date	userid	compid	res64	spent (GHz-days)
2000-09-08T00:00:00	ANONYMOUS	v4_computers	6381AEC59BBC1BC1	0.877

date

userid

compid

res64

spent (GHz-days)

2000-09-08T00:00:00

ANONYMOUS

v4_computers

6381AEC59BBC1BC1

0.877

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 = 2000000, B2 = 112000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 175000, B2 = 3937500 (P-1 stage 2)

B1 = 175000 (P-1 stage 1)

B1 = 65000, B2 = 1121250 (P-1 stage 2)

B1 = 65000 (P-1 stage 1)

B1 = 25000, B2 = 156250 (P-1 stage 2)

B1 = 25000 (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