M1865551 Mersenne number exponent details

Residue

Status

L-L

D2F34E9F166ADDC1

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	15.9277	68.6567%	500000	15000000	0.1015	5.0803%	16.0292	70.2491%	1.5923%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0278%	0.0116	64.2734%	1.1155%
GPU72	2⁶¹	0.1647	65.5738%	10000	150000	0.0014	1.6888%	0.1660	66.1552%	0.5814%
Difference	+6	+15.7630	+3.0829%	+490000	+14850000	+0.1001	+3.3915%	+15.8631	+4.0939%	+4.0939%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9277

68.6567%

500000

15000000

0.1015

5.0803%

16.0292

70.2491%

1.5923%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0278%

0.0116

64.2734%

1.1155%

GPU72

2⁶¹

0.1647

65.5738%

10000

150000

0.0014

1.6888%

0.1660

66.1552%

0.5814%

Difference

+15.7630

+3.0829%

+490000

+14850000

+0.1001

+3.3915%

+15.8631

+4.0939%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1865551	25301859615022849943737	23	74.422	6781336885194468 2² × 3 × 7741367 × 72998917	2013-02-12	7741367	72998917	2,418.4	0.8886	1.2393

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1865551

25301859615022849943737

74.422

6781336885194468
2² × 3 × 7741367 × 72998917

2013-02-12

7741367

72998917

2,418.4

0.8886

1.2393

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-07T14:22:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.926%
2016-03-16T12:37:29	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.080%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2010-04-06T12:16:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.082	-	-
2011-03-08T05:14:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.856	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.570 GHz-days
Estimated T-Level:	24.554

Digits	B1	Curves	Complete	FacMiss
20	11000	255 / 100	2.550	7.709%
25	50000	255 / 280	0.911	40.158%

New Calculation Method

Total ECM effort:	19.570 GHz-days
Estimated T-Level:	24.554

Digits	B1	Complete	FacMiss
20	11000	10.503	0.003%
25	50000	0.967	38.036%
30	250000	0.061	94.050%
35	1000000	0.003	99.712%

ECM Summary

B1	B2	factor	curves	GHz-days
		25301859615022849943737	1	0.00000e+0
50000	5000000		38	2.630
50000	6600000		217	16.94

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-28T00:15:00	Rob_Dee	twopc	50000	5000000						1	0.069
2009-06-30T05:28:00	borkencode	CFF2DC1CD	50000	5000000						3	0.208
2010-04-19T12:50:00	James Hintz	nana	50000	5000000						3	0.208
2011-07-22T17:39:00	S36049	Wolle5	50000	5000000						3	0.208
2013-02-12T21:27:00	Xyzzy	J			25301859615022849943737	74.422		1		1	-
2020-10-20T04:35:58	nordi	sweet16	50000	5000000						7	0.485
2021-01-11T17:22:26	Lisander Viaene		50000	5000000						7	0.485
2021-04-05T10:04:03	Chang Chia-Tche	exbpc13	50000	5000000						7	0.485
2021-07-18T19:36:41	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.485
2021-09-03T08:16:49	TJAOI	Manual testing	50000	6600000						217	16.94

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	D2F34E9F166ADDC1	0.101

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

D2F34E9F166ADDC1

0.101

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 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

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