M17256787 Mersenne number exponent details

Residue

Status

L-L

EC9CF26AC87D0A81

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	1.7219	62.6866%	430000	9000000	0.7406	5.9238%	2.4624	64.8969%	2.2104%
PrimeNet	2⁶⁵	0.4228	61.5385%	80000	2400000	0.1704	4.5397%	0.5932	63.2845%	1.7460%
GPU72	2⁶⁹	6.9183	63.7681%	120000	3200000	0.2376	3.3024%	7.1559	64.9646%	1.1965%
Difference	-2	-5.1964	-1.0815%	+310000	+5800000	+0.5029	+2.6214%	-4.6934	-0.0677%	-0.0677%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.7219

62.6866%

430000

9000000

0.7406

5.9238%

2.4624

64.8969%

2.2104%

PrimeNet

2⁶⁵

0.4228

61.5385%

80000

2400000

0.1704

4.5397%

0.5932

63.2845%

1.7460%

GPU72

2⁶⁹

6.9183

63.7681%

120000

3200000

0.2376

3.3024%

7.1559

64.9646%

1.1965%

Difference

-2

-5.1964

-1.0815%

+310000

+5800000

+0.5029

+2.6214%

-4.6934

-0.0677%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
17256787	43608471359327145160471	23	75.207	1263516532924905 3² × 5 × 7⁴ × 11694354509	2017-12-27	2401	11694354509	453.49	526.09	982.58

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

17256787

43608471359327145160471

75.207

1263516532924905
3² × 5 × 7⁴ × 11694354509

2017-12-27

2401

11694354509

453.49

526.09

982.58

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-12-02T00:00:00	Ryan Malayter	v4_computers	275000	275000		-		-	-	0.227	-	-	2.172%
2017-06-12T21:26:48	riccardo uberti	Duallie-2	430000	9000000	12	-		-	-	0.741	-	-	5.924%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-02-18T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.002	-	-
2001-04-01T00:00:00	Net_Force	v4_computers	2¹	2⁵⁹		-	-	0.004	-	-
2001-08-24T00:00:00	tsc	v4_computers	2¹	2⁶⁵		-	-	0.423	-	-
2013-09-23T23:50:00	David Campeau	Manual testing	2⁶⁵	2⁶⁶		-	-	0.433	-	-
2014-09-05T00:08:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.866	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.866 GHz-days
Estimated T-Level:	0.050

Digits	B1	Curves	Complete	FacMiss
20	11000	1 / 100	0.010	99.000%
25	50000	1 / 280	0.004	99.643%

New Calculation Method

Total ECM effort:	0.866 GHz-days
Estimated T-Level:	0.050

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	43608471359327145160471	1	0.866

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-27T21:21:27	Sid & Andy	Etch	50000	5000000	43608471359327145160471	75.207	1	2		1	0.866

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2003-01-16T00:00:00	Ryan Malayter	v4_computers	EC9CF26AC87D0A81	9.83
2006-05-29T00:00:00	ANONYMOUS	v4_computers	EC9CF26AC87D0A81	9.83

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-10-03T19:23:13

riccardo uberti

Nomad2C

43608471359327145160471

792B7D94A2BC7BC7

2020-08-08T04:41:30

Jaytholomew

43608471359327145160471

792B7D94A2BC7BC7

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 = 430000, B2 = 9000000 (P-1 stage 2)

B1 = 430000 (P-1 stage 1)

B1 = 275000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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