M2186651 Mersenne number exponent details

Residue

Status

L-L

42E5F8628CEC1987

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	13.5888	67.1642%	500000	15000000	0.1230	5.1783%	13.7118	68.8645%	1.7003%
PrimeNet	2⁵⁸	0.0176	62.0690%	10000	180000	0.0018	2.8599%	0.0194	63.1537%	1.0848%
GPU72	2⁶²	0.2810	64.5161%	11000	160000	0.0018	1.5697%	0.2828	65.0731%	0.5570%
Difference	+5	+13.3078	+2.6481%	+489000	+14840000	+0.1212	+3.6086%	+13.4290	+3.7914%	+3.7914%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.5888

67.1642%

500000

15000000

0.1230

5.1783%

13.7118

68.8645%

1.7003%

PrimeNet

2⁵⁸

0.0176

62.0690%

10000

180000

0.0018

2.8599%

0.0194

63.1537%

1.0848%

GPU72

2⁶²

0.2810

64.5161%

11000

160000

0.0018

1.5697%

0.2828

65.0731%

0.5570%

Difference

+13.3078

+2.6481%

+489000

+14840000

+0.1212

+3.6086%

+13.4290

+3.7914%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2186651	367056681796038077462249	24	78.280	83931245040026524 2² × 7² × 2845639 × 150483121	2008-12-25	2845639	150483121	53,107	1.0382	1.4599

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2186651

367056681796038077462249

78.280

83931245040026524
2² × 7² × 2845639 × 150483121

2008-12-25

2845639

150483121

53,107

1.0382

1.4599

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.280%
2016-03-28T11:47:17	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.178%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.551 GHz-days
Estimated T-Level:	0.850

Digits	B1	Curves	Complete	FacMiss
20	11000	17 / 100	0.170	84.294%
25	50000	17 / 280	0.061	94.099%

New Calculation Method

Total ECM effort:	1.551 GHz-days
Estimated T-Level:	0.850

Digits	B1	Complete	FacMiss
20	11000	0.676	50.850%
25	50000	0.063	93.921%
30	250000	0.004	99.604%

ECM Summary

B1	B2	factor	curves	GHz-days
		367056681796038077462249	1	0.00000e+0
50000	5000000		10	0.855
50000	6968266		7	0.696

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-25T04:43:00	ksims	ZhViZCJBe1505			367056681796038077462249	78.280		1		1	-
2018-12-17T07:20:24	Oliver Kruse	HTC5	50000	5000000						3	0.257
2022-05-12T03:18:56	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.599
2022-07-05T11:56:34	debrouxl	dl380g9-1	50000	6968266						7	0.696

date	userid	compid	res64	spent (GHz-days)
1999-02-14T00:00:00	ANONYMOUS	v4_computers	42E5F8628CEC1987	0.144

date

userid

compid

res64

spent (GHz-days)

1999-02-14T00:00:00

ANONYMOUS

v4_computers

42E5F8628CEC1987

0.144

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-09T05:51:52

Oliver Kruse

GTX-3

367056681796038077462249

993EF7EDD45C5B__

2017-11-19T10:21:34

kkmrkkblmbrbk

c4.xlarge

367056681796038077462249

993EF7EDD45C5B__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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