M6005141 Mersenne number exponent details

Residue

Status

L-L

A2DCCF4502CE634A

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	2⁶⁸	9.9256	66.1765%	1250000	50000000	1.0037	7.1811%	10.9294	68.6054%	2.4289%
PrimeNet	2⁶²	0.1023	62.9032%	26000	600000	0.0147	3.3302%	0.1170	64.1386%	1.2354%
GPU72	2⁶⁶	2.4593	65.1515%	40000	900000	0.0223	2.4175%	2.4816	65.9940%	0.8425%
Difference	+2	+7.4663	+1.0250%	+1210000	+49100000	+0.9814	+4.7636%	+8.4478	+2.6114%	+2.6114%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

9.9256

66.1765%

1250000

50000000

1.0037

7.1811%

10.9294

68.6054%

2.4289%

PrimeNet

2⁶²

0.1023

62.9032%

26000

600000

0.0147

3.3302%

0.1170

64.1386%

1.2354%

GPU72

2⁶⁶

2.4593

65.1515%

40000

900000

0.0223

2.4175%

2.4816

65.9940%

0.8425%

Difference

+7.4663

+1.0250%

+1210000

+49100000

+0.9814

+4.7636%

+8.4478

+2.6114%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
6005141	24528116686524664616967961097537	32	104.274	2042259847564334011222048 2⁵ × 11 × 29² × 283 × 33809 × 325463 × 2215399	2017-09-22	325463	2215399	2.311e+10	0.1101	0.1702

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

6005141

24528116686524664616967961097537

104.274

2042259847564334011222048
2⁵ × 11 × 29² × 283 × 33809 × 325463 × 2215399

2017-09-22

325463

2215399

2.311e+10

0.1101

0.1702

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-11-05T00:00:00	ANONYMOUS	v4_computers	25000	25000		-		-	-	0.006	-	-	0.385%
2011-03-18T06:07:00	markr	tiny	110000	2172500		-		-	-	0.057	-	-	2.867%
2017-09-22T08:37:43	mikr	S067	1250000	50000000	12		24528116686524664616967961097537	32	104.274	1.004	2.128	2.007	7.181%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.051	-	-
1998-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶²		-	-	0.102	-	-
2016-02-23T16:39:15	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.163	-	-
2014-01-05T16:11:00	kracker	Manual testing	2⁶³	2⁶⁴		-	-	0.327	-	-
2014-01-05T21:55:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.622	-	-
2015-09-29T13:19:01	Bruno Victal	Manual testing	2⁶⁵	2⁶⁶		-	-	1.244	-	-
2016-03-09T01:41:53	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	2.489	-	-
2017-09-20T17:55:13	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	4.978	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Curves	Complete	FacMiss
20	11000	6 / 100	0.060	94.148%
25	50000	6 / 280	0.021	97.876%

New Calculation Method

Total ECM effort:	1.617 GHz-days
Estimated T-Level:	0.300

Digits	B1	Complete	FacMiss
20	11000	0.194	82.403%
25	50000	0.017	98.266%
30	250000	0.001	99.892%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		6	1.617

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2011-07-16T11:52:00	JimBa	Dell	50000	5000000						3	0.808
2016-06-26T22:58:20	mensasnem	thomas	50000	5000000						3	0.808

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	A2DCCF4502CE634A	1.064
2000-12-07T00:00:00	ANONYMOUS	v4_computers	A2DCCF4502CE634A	1.064

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-12-13T12:23:29

Oliver Kruse

Threadripper

24528116686524664616967961097537

A8B6FE143B2CF7__

2018-05-03T00:51:23

kkmrkkblmbrbk

c5.large

24528116686524664616967961097537

A8B6FE143B2CF7__

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 = 1250000, B2 = 50000000 (P-1 stage 2)

B1 = 1250000 (P-1 stage 1)

B1 = 110000, B2 = 2172500 (P-1 stage 2)

B1 = 110000 (P-1 stage 1)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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