M15277601 Mersenne number exponent details

Residue

Status

L-L

5E61A0F21400F97D

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	1.9449	64.1791%	300000	6000000	0.4440	5.1929%	2.3889	66.0393%	1.8602%
PrimeNet	2⁶⁵	0.4775	63.0769%	70000	2200000	0.1353	4.2900%	0.6128	64.6609%	1.5840%
GPU72	2⁶⁹	7.8145	65.2174%	100000	2600000	0.1718	3.0014%	7.9863	66.2614%	1.0440%
Difference	-2	-5.8696	-1.0383%	+200000	+3400000	+0.2722	+2.1915%	-5.5973	-0.2221%	-0.2221%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1.9449

64.1791%

300000

6000000

0.4440

5.1929%

2.3889

66.0393%

1.8602%

PrimeNet

2⁶⁵

0.4775

63.0769%

70000

2200000

0.1353

4.2900%

0.6128

64.6609%

1.5840%

GPU72

2⁶⁹

7.8145

65.2174%

100000

2600000

0.1718

3.0014%

7.9863

66.2614%

1.0440%

Difference

-2

-5.8696

-1.0383%

+200000

+3400000

+0.2722

+2.1915%

-5.5973

-0.2221%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15277601	95061337470839799489247	23	76.331	3111134315879823 3 × 2251 × 75167 × 6129073	2016-12-04	75167	6129073	1,887.0	0.2945	0.4536

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15277601

95061337470839799489247

76.331

3111134315879823
3 × 2251 × 75167 × 6129073

2016-12-04

75167

6129073

1,887.0

0.2945

0.4536

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-31T00:00:00	ANONYMOUS	v4_computers	225000	225000		-		-	-	0.164	-	-	1.952%
2016-10-02T00:33:09	Tha	Manual testing	300000	6000000	12	-		-	-	0.444	-	-	5.193%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-01-08T00:00:00	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2001-01-08T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.003	-	-
2001-02-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.478	-	-
2016-03-16T02:28:24	Mark Rose	Manual testing	2⁶⁵	2⁶⁶		-	-	0.489	-	-
2014-05-28T13:19:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.978	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.763 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:	0.763 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	95061337470839799489247	1	0.763

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-12-04T18:58:04	ATH	xps	50000	5000000	95061337470839799489247	76.331	1	2		1	0.763

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-06-09T00:00:00	ANONYMOUS	v4_computers	5E61A0F21400F97D	7.662
2006-02-15T00:00:00	ebravick	v4_computers	5E61A0F21400F97D	7.662

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 = 300000, B2 = 6000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 225000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

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