M1461913 Mersenne number exponent details

Residue

Status

L-L

528D07C9277DDCD0

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	20.3254	68.6567%	500000	15000000	0.0714	4.9330%	20.3968	70.2029%	1.5462%
PrimeNet	2⁵⁶	0.0066	62.5000%	7000	120000	0.0007	2.9087%	0.0073	63.5908%	1.0908%
GPU72	2⁶⁰	0.1051	65.0000%	6500	90000	0.0006	1.3989%	0.1057	65.4896%	0.4896%
Difference	+7	+20.2203	+3.6567%	+493500	+14910000	+0.0708	+3.5341%	+20.2911	+4.7133%	+4.7133%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.3254

68.6567%

500000

15000000

0.0714

4.9330%

20.3968

70.2029%

1.5462%

PrimeNet

2⁵⁶

0.0066

62.5000%

7000

120000

0.0007

2.9087%

0.0073

63.5908%

1.0908%

GPU72

2⁶⁰

0.1051

65.0000%

6500

90000

0.0006

1.3989%

0.1057

65.4896%

0.4896%

Difference

+20.2203

+3.6567%

+493500

+14910000

+0.0708

+3.5341%

+20.2911

+4.7133%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1461913	85512270767277455630857	23	76.179	29246703041589156 2² × 3² × 17 × 1049 × 2749 × 16572013	2009-01-24	2749	16572013	12,317	0.0501	0.0934
1461913	4513607949771035047332889	25	81.901	1543733433443383788 2² × 3 × 20177 × 138101 × 46167637	2019-04-12	138101	46167637	412,435	0.1465	0.2601

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1461913

85512270767277455630857

76.179

29246703041589156
2² × 3² × 17 × 1049 × 2749 × 16572013

2009-01-24

2749

16572013

12,317

0.0501

0.0934

1461913

4513607949771035047332889

81.901

1543733433443383788
2² × 3 × 20177 × 138101 × 46167637

2019-04-12

138101

46167637

412,435

0.1465

0.2601

exponent	prime factors	composite factor	digits	bits*
1461913	85512270767277455630857 4513607949771035047332889	385968865138156810562521558250119466572779355873	48	158.079

exponent

prime factors

composite factor

digits

bits*

1461913

85512270767277455630857
4513607949771035047332889

385968865138156810562521558250119466572779355873

158.079

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	15000	243750		-		-	-	0.002	-	-	0.840%
2016-03-17T19:14:39	alpertron	Manual testing	500000	15000000	12	-		-	-	0.071	-	-	4.933%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.013	-	-
2003-07-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.026	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.480 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	26.480 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.674	18.740%
30	250000	0.144	86.623%
35	1000000	0.010	99.005%

ECM Summary

B1	B2	factor	curves	GHz-days
		85512270767277455630857	1	0.00000e+0
50000	5000000		185	8.770
50000	5000000	4513607949771035047332889	66	3.129
250000	40000000		50	14.58

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T12:46:00	Steve Scott	Abit	50000	5000000						1	0.047
2009-01-05T17:06:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.142
2009-01-24T10:48:00	axn	Manual testing			85512270767277455630857	76.179		1		1	-
2018-11-25T11:22:39	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-04-12T15:20:52	TJAOI	Manual testing	50000	5000000	4513607949771035047332889	81.901	66	2		66	3.129
2019-04-12T15:20:52	TJAOI	Manual testing	50000	5000000						178	8.438
2022-04-07T09:47:15	TJAOI	Manual testing	250000	40000000						50	14.58

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	528D07C9277DDCD0	0.056

date

userid

compid

res64

spent (GHz-days)

1998-12-27T00:00:00

ANONYMOUS

v4_computers

528D07C9277DDCD0

0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T03:18:54

Oliver Kruse

GTX-2

85512270767277455630857

E4C936407044D3__

2017-10-27T22:36:32

kkmrkkblmbrbk

old

85512270767277455630857

E4C936407044D3__

2019-04-12T16:05:07

ATH

ec2-PRPCF

85512270767277455630857

4513607949771035047332889

E8AFE4E4E537C195

2019-04-13T17:35:27

kkmrkkblmbrbk

c5.large

85512270767277455630857

4513607949771035047332889

E8AFE4E4E537C195

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 = 15000, B2 = 243750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

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