M1436257 Mersenne number exponent details

Residue

Status

L-L

CF2BE8C038D49DED

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	20.6884	68.6567%	500000	15000000	0.0714	4.9225%	20.7599	70.1996%	1.5429%
PrimeNet	2⁵⁶	0.0067	62.5000%	6500	110000	0.0007	2.7759%	0.0074	63.5410%	1.0410%
GPU72	2⁶⁰	0.1069	65.0000%	6000	90000	0.0006	1.3543%	0.1075	65.4740%	0.4740%
Difference	+7	+20.5815	+3.6567%	+494000	+14910000	+0.0708	+3.5681%	+20.6523	+4.7256%	+4.7256%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.6884

68.6567%

500000

15000000

0.0714

4.9225%

20.7599

70.1996%

1.5429%

PrimeNet

2⁵⁶

0.0067

62.5000%

6500

110000

0.0007

2.7759%

0.0074

63.5410%

1.0410%

GPU72

2⁶⁰

0.1069

65.0000%

6000

90000

0.0006

1.3543%

0.1075

65.4740%

0.4740%

Difference

+20.5815

+3.6567%

+494000

+14910000

+0.0708

+3.5681%

+20.6523

+4.7256%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1436257	1241629861852151063	19	60.107	432245016683 65479 × 6601277	2008-12-16	65479	6601277	0.1519	0.0233	0.0372

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1436257

1241629861852151063

60.107

432245016683
65479 × 6601277

2008-12-16

65479

6601277

0.1519

0.0233

0.0372

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	-	-	0.837%
2016-03-17T19:14:18	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1241629861852151063	-	-	0.071	-	-	4.922%

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	-	-
2003-07-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.027	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.344 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	298 / 100	2.980	5.004%
25	50000	298 / 280	1.064	34.432%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.344 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.538	0.000%
25	50000	1.640	19.395%
30	250000	0.140	86.925%
35	1000000	0.010	99.024%

ECM Summary

B1	B2	factor	curves	GHz-days
		1241629861852151063	1	0.00000e+0
50000	5000000		248	11.72
250000	35000000		50	13.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-05T06:42:00	James Heinrich	WHS	50000	5000000						1	0.047
2008-12-16T18:42:00	ksims	ZhViZCJBe1505			1241629861852151063	60.107		1		1	-
2018-11-24T16:59:49	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-02-22T12:21:53	TJAOI	Manual testing	50000	5000000						244	11.53
2021-09-29T12:09:30	TJAOI	Manual testing	250000	35000000						50	13.62

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T23:07:17

Oliver Kruse

GTX-3

1241629861852151063

5A60EA23DFD3B8__

2017-10-27T02:33:54

kkmrkkblmbrbk

c4.xlarge

1241629861852151063

5A60EA23DFD3B8__

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)

10³

10⁴

10⁵

10⁶

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