M4961941 Mersenne number exponent details

Residue

Status

L-L

76B649EC9D41B0C6

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	5.9884	65.6716%	1200000	43100000	0.7000	7.4625%	6.6884	68.2334%	2.5618%
PrimeNet	2⁶¹	0.0619	62.2951%	22000	450000	0.0091	3.3090%	0.0710	63.5427%	1.2477%
GPU72	2⁶⁵	1.4703	64.6154%	34000	700000	0.0141	2.4129%	1.4845	65.4692%	0.8538%
Difference	+2	+4.5180	+1.0563%	+1166000	+42400000	+0.6859	+5.0496%	+5.2039	+2.7642%	+2.7642%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

5.9884

65.6716%

1200000

43100000

0.7000

7.4625%

6.6884

68.2334%

2.5618%

PrimeNet

2⁶¹

0.0619

62.2951%

22000

450000

0.0091

3.3090%

0.0710

63.5427%

1.2477%

GPU72

2⁶⁵

1.4703

64.6154%

34000

700000

0.0141

2.4129%

1.4845

65.4692%

0.8538%

Difference

+4.5180

+1.0563%

+1166000

+42400000

+0.6859

+5.0496%

+5.2039

+2.7642%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4961941	10014936532888293604442468791	29	93.016	1009175293790100850095 3² × 5 × 41 × 30427 × 990799 × 18143687	2015-04-04	990799	18143687	437,080,729	0.3870	0.4053

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4961941

10014936532888293604442468791

93.016

1009175293790100850095
3² × 5 × 41 × 30427 × 990799 × 18143687

2015-04-04

990799

18143687

437,080,729

0.3870

0.4053

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-08-23T18:33:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	1.575%
2011-07-25T18:37:00	Squeeky_Squirrel	T7500_2200	60000	975000		-		-	-	0.022	-	-	2.301%
2015-04-04T08:49:00	mikr	MSI	1200000	43100000	12		10014936532888293604442468791	29	93.016	0.700	1.376	1.400	7.463%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.062	-	-
2009-12-20T04:55:00	markr	rmst	2⁶¹	2⁶²		-	-	0.062	-	-
2011-11-13T15:25:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.322	-	-
2014-12-29T19:38:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.396	-	-
2014-12-29T19:38:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	0.753	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.262 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:	1.262 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	1.262

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-05-23T16:27:00	Lukasz Wrobel	4_x_4	50000	5000000						3	0.631
2014-04-13T01:53:00	S36049	Wolle6	50000	5000000						3	0.631

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-01T00:00:00	James D-P	v4_computers	76B649EC9D41B0C6	0.688
2000-04-19T00:00:00	ANONYMOUS	v4_computers	76B649EC9D41B0C6	0.688

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T17:04:24

kkmrkkblmbrbk

Manual testing

10014936532888293604442468791

9C20CFBB7BB174__

2018-04-18T07:01:26

ATH

work200557

10014936532888293604442468791

9C20CFBB7BB174__

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 = 1200000, B2 = 43100000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 60000, B2 = 975000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 30000, B2 = 435000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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