M13782551 Mersenne number exponent details

Residue

Status

L-L

754EC501441D7535

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	2⁷⁰	17.3372	65.7143%	155000	2983750	0.1989	2.9403%	17.5361	66.7224%	1.0081%
PrimeNet	2⁶⁵	0.5293	63.0769%	60000	1900000	0.1031	3.9928%	0.6324	64.5512%	1.4743%
GPU72	2⁶⁹	8.6622	65.2174%	90000	2200000	0.1319	2.7911%	8.7940	66.1882%	0.9708%
Difference	+1	+8.6750	+0.4969%	+65000	+783750	+0.0670	+0.1493%	+8.7420	+0.5342%	+0.5342%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

17.3372

65.7143%

155000

2983750

0.1989

2.9403%

17.5361

66.7224%

1.0081%

PrimeNet

2⁶⁵

0.5293

63.0769%

60000

1900000

0.1031

3.9928%

0.6324

64.5512%

1.4743%

GPU72

2⁶⁹

8.6622

65.2174%

90000

2200000

0.1319

2.7911%

8.7940

66.1882%

0.9708%

Difference

+8.6750

+0.4969%

+65000

+783750

+0.0670

+0.1493%

+8.7420

+0.5342%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13782551	1603140628843474771409	22	70.441	58158341980504 2³ × 1709 × 4253828407	2021-09-04	1709	4253828407	18.479	149.10	278.48

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

13782551

1603140628843474771409

70.441

58158341980504
2³ × 1709 × 4253828407

2021-09-04

1709

4253828407

18.479

149.10

278.48

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-03-01T00:00:00	dave_0273	v4_computers	80000	1400000		-		-	-	0.098	-	-	2.172%
2015-06-30T00:04:00	Sid & Andy	Speck	155000	2983750		-		-	-	0.199	-	-	2.940%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.529	-	-
2014-07-02T04:17:00	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.542	-	-
2015-08-20T10:16:00	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.084	-	-
2017-12-22T13:48:42	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.169	-	-
2018-01-14T22:55:33	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.338	-	-
2021-08-08T08:14:49	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.675	-	-
2021-09-04T06:49:36	SRBase	Manual testing	2⁷⁰	2⁷¹*	1603140628843474771409	70.441	22	1.142	12.43	2.320

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.675 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:	0.675 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	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-04T02:57:43	Summy	RG03	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2005-04-11T00:00:00	ANONYMOUS	v4_computers	754EC501441D7535	6.115

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 = 155000, B2 = 2983750 (P-1 stage 2)

B1 = 155000 (P-1 stage 1)

B1 = 80000, B2 = 1400000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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