M15105869 Mersenne number exponent details

Residue

Status

L-L

FECAD50B387BBBED

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	2⁷²	63.3087	66.6667%	185000	4440000	0.3031	2.6867%	63.6119	67.5622%	0.8956%
PrimeNet	2⁶⁵	0.4830	63.0769%	65000	2000000	0.1239	4.1472%	0.6069	64.6082%	1.5313%
GPU72	2⁶⁹	7.9033	65.2174%	100000	2600000	0.1718	2.9964%	8.0751	66.2596%	1.0422%
Difference	+3	+55.4054	+1.4493%	+85000	+1840000	+0.1313	-0.3097%	+55.5368	+1.3026%	+1.3026%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

63.3087

66.6667%

185000

4440000

0.3031

2.6867%

63.6119

67.5622%

0.8956%

PrimeNet

2⁶⁵

0.4830

63.0769%

65000

2000000

0.1239

4.1472%

0.6069

64.6082%

1.5313%

GPU72

2⁶⁹

7.9033

65.2174%

100000

2600000

0.1718

2.9964%

8.0751

66.2596%

1.0422%

Difference

+55.4054

+1.4493%

+85000

+1840000

+0.1313

-0.3097%

+55.5368

+1.3026%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
15105869	91307695363934649517961	23	76.273	3022258943326420 2² × 5 × 7 × 21587563880903	2022-02-22	7	21587563880903	1,627.1	855,314	1,597,489

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

15105869

91307695363934649517961

76.273

3022258943326420
2² × 5 × 7 × 21587563880903

2022-02-22

21587563880903

1,627.1

855,314

1,597,489

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-16T00:00:00	ANONYMOUS	v4_computers	185000	4440000		-		-	-	0.303	-	-	2.687%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2022-02-22T08:48:38	ATH	ec2-P_1	1000000	29000000	2	7	91307695363934649517961	P+1	23	76.273	2.094

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-12-31T00:00:00	Net_Force	v4_computers	2¹	2⁵⁷		-	-	0.001	-	-
2000-12-31T00:00:00	Net_Force	v4_computers	2¹	2⁵⁸		-	-	0.003	-	-
2001-01-28T00:00:00	schaz	v4_computers	2¹	2⁶⁵		-	-	0.483	-	-
2014-05-14T07:05:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.495	-	-
2014-05-14T07:05:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	0.989	-	-
2016-11-16T01:10:14	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	1.979	-	-
2017-10-08T22:00:39	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	3.958	-	-
2021-06-27T22:13:31	lycorn	Manual testing	2⁶⁹	2⁷⁰		-	-	7.915	-	-
2021-09-06T18:03:25	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	15.83	-	-
2021-10-15T18:41:41	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	31.66	-	-

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	0.032	96.826%
25	50000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.763

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-27T18:29:14	Bruce	test	50000	5000000						1	0.763

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-24T00:00:00	ANONYMOUS	v4_computers	FECAD50B387BBBED	7.576
2005-09-22T00:00:00	ANONYMOUS	v4_computers	FECAD50B387BBBED	7.576

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 = 1000000, B2 = 29000000 (P+1 stage 2)

B1 = 1000000 (P+1 stage 1)

B1 = 185000, B2 = 4440000 (P-1 stage 2)

B1 = 185000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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