M9636421 Mersenne number exponent details

Residue

Status

L-L

9A82B66D0C13A9D3

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	2⁶⁷	3.0835	64.1791%	115000	2185000	0.0963	3.4712%	3.1798	65.4225%	1.2434%
PrimeNet	2⁶⁴	0.3694	62.5000%	40000	1100000	0.0413	3.5084%	0.4107	63.8156%	1.3156%
GPU72	2⁶⁸	6.1854	64.7059%	60000	1400000	0.0563	2.4695%	6.2416	65.5775%	0.8716%
Difference	-1	-3.1019	-0.5268%	+55000	+785000	+0.0401	+1.0017%	-3.0618	-0.1550%	-0.1550%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

3.0835

64.1791%

115000

2185000

0.0963

3.4712%

3.1798

65.4225%

1.2434%

PrimeNet

2⁶⁴

0.3694

62.5000%

40000

1100000

0.0413

3.5084%

0.4107

63.8156%

1.3156%

GPU72

2⁶⁸

6.1854

64.7059%

60000

1400000

0.0563

2.4695%

6.2416

65.5775%

0.8716%

Difference

-1

-3.1019

-0.5268%

+55000

+785000

+0.0401

+1.0017%

-3.0618

-0.1550%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
9636421	599988466715054862566879	24	78.989	31131291727242659 719 × 99289 × 436080949	2014-11-11	99289	436080949	9,568.8	10.088	18.767

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

9636421

599988466715054862566879

78.989

31131291727242659
719 × 99289 × 436080949

2014-11-11

99289

436080949

9,568.8

10.088

18.767

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:56:00	Carsten Kossendey	leela	55000	852500		-		-	-	0.042	-	-	2.430%
2013-02-11T09:47:00	Nesowa	EPC	115000	2185000		-		-	-	0.096	-	-	3.471%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-05-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.369	-	-
2013-08-28T07:17:00	Nesowa	Manual testing	2⁶⁴	2⁶⁵		-	-	0.388	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.331 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	1.331 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	599988466715054862566879	3	1.331

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-11-11T02:10:00	JimBa	Dell	50000	5000000	599988466715054862566879	78.989	3	2		3	1.331

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2000-04-12T00:00:00	ANONYMOUS	v4_computers	9A82B66D0C13A9D3	2.811
2003-06-09T00:00:00	ANONYMOUS	v4_computers	9A82B66D0C13A9D3	2.811

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-06T11:00:28

mnd9

75204b

599988466715054862566879

B9845562269D21__

2020-12-18T08:39:33

kutens

spica-b

599988466715054862566879

B9845562269D215F

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 = 115000, B2 = 2185000 (P-1 stage 2)

B1 = 115000 (P-1 stage 1)

B1 = 55000, B2 = 852500 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

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