M1461851 Mersenne number exponent details

Residue

Status

L-L

68DA620F0D20BA21

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	20.3262	68.6567%	500000	15000000	0.0714	4.9330%	20.3976	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	+20.2212	+3.6567%	+493500	+14910000	+0.0708	+3.5341%	+20.2920	+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

20.3262

68.6567%

500000

15000000

0.0714

4.9330%

20.3976

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

+20.2212

+3.6567%

+493500

+14910000

+0.0708

+3.5341%

+20.2920

+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
1461851	12835522083490571503	20	63.477	4390160858901 3² × 137 × 6563 × 542519	2009-01-24	6563	542519	1.3072	0.0020	0.0031

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1461851

12835522083490571503

63.477

4390160858901
3² × 137 × 6563 × 542519

2009-01-24

6563

542519

1.3072

0.0020

0.0031

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%
2016-03-17T19:14:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 12835522083490571503	-	-	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
		12835522083490571503	1	0.00000e+0
50000	5000000		251	11.90
250000	40000000		50	14.58

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-01-06T12:09:00	Squeeky_Squirrel	P4_2600	50000	5000000						1	0.047
2009-01-01T18:27:00	Smurgs	Praca	50000	5000000						3	0.142
2009-01-24T06:44:00	axn	Manual testing			12835522083490571503	63.477		1		1	-
2018-11-25T10:35:39	Chang Chia-Tche	exbpc13	50000	5000000						3	0.142
2019-04-12T15:20:51	TJAOI	Manual testing	50000	5000000						244	11.57
2022-04-07T09:47:14	TJAOI	Manual testing	250000	40000000						50	14.58

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	PHeede	v4_computers	68DA620F0D20BA21	0.056

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

PHeede

v4_computers

68DA620F0D20BA21

0.056

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T03:23:21

Oliver Kruse

GTX-2

12835522083490571503

B5F25A00A7C9A4__

2017-11-05T00:23:05

kkmrkkblmbrbk

c4.xlarge

12835522083490571503

B5F25A00A7C9A4__

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