M4939751 Mersenne number exponent details

Residue

Status

L-L

6BABE734AF61E311

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	6.0153	65.6716%	1200000	39750000	0.6633	7.3609%	6.6786	68.1985%	2.5269%
PrimeNet	2⁶¹	0.0622	62.2951%	22000	450000	0.0091	3.3066%	0.0713	63.5418%	1.2467%
GPU72	2⁶⁵	1.4769	64.6154%	34000	700000	0.0141	2.4111%	1.4911	65.4685%	0.8532%
Difference	+2	+4.5383	+1.0563%	+1166000	+39050000	+0.6492	+4.9498%	+5.1875	+2.7300%	+2.7300%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.0153

65.6716%

1200000

39750000

0.6633

7.3609%

6.6786

68.1985%

2.5269%

PrimeNet

2⁶¹

0.0622

62.2951%

22000

450000

0.0091

3.3066%

0.0713

63.5418%

1.2467%

GPU72

2⁶⁵

1.4769

64.6154%

34000

700000

0.0141

2.4111%

1.4911

65.4685%

0.8532%

Difference

+4.5383

+1.0563%

+1166000

+39050000

+0.6492

+4.9498%

+5.1875

+2.7300%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4939751	12182024095485966133511257201	29	93.299	1233060542473291278600 2³ × 3 × 5² × 7 × 293 × 983 × 762017 × 1337671	2014-12-05	762017	1337671	738,332,508	0.1595	0.3117

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4939751

12182024095485966133511257201

93.299

1233060542473291278600
2³ × 3 × 5² × 7 × 293 × 983 × 762017 × 1337671

2014-12-05

762017

1337671

738,332,508

0.1595

0.3117

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-09-14T17:07:00	Carsten Kossendey	durandal	30000	435000		-		-	-	0.010	-	-	1.574%
2011-07-18T11:48:00	Squeeky_Squirrel	T7500_2200	60000	960000		-		-	-	0.022	-	-	2.290%
2014-12-05T12:35:00	mikr	MSI	1200000	39750000	12		12182024095485966133511257201	29	93.299	0.663	1.369	1.327	7.361%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.062	-	-
2010-03-21T05:54:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.062	-	-
2011-09-28T18:57:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.323	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.261 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:	1.261 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	1.261

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-05-11T20:25:00	Lupo	tower	50000	5000000						3	0.630
2014-04-01T21:44:00	timc995	t410	50000	5000000						3	0.630

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-05-23T00:00:00	ANONYMOUS	v4_computers	6BABE734AF61E311	0.685
2000-04-05T00:00:00	ANONYMOUS	v4_computers	6BABE734AF61E311	0.685

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T16:59:35

kkmrkkblmbrbk

Manual testing

12182024095485966133511257201

37BC9CB7BCDE10__

2018-04-13T16:16:31

ATH

ec2-PRPCFDC

12182024095485966133511257201

37BC9CB7BCDE10__

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 = 39750000 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

B1 = 60000, B2 = 960000 (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