M2238947 Mersenne number exponent details

Residue

Status

L-L

7839C75D6CAA7AAD

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	13.2714	67.1642%	500000	15000000	0.1230	5.1930%	13.3944	68.8693%	1.7052%
PrimeNet	2⁵⁸	0.0171	62.0690%	10000	180000	0.0018	2.8723%	0.0190	63.1585%	1.0895%
GPU72	2⁶²	0.2744	64.5161%	11000	190000	0.0020	1.6583%	0.2764	65.1046%	0.5884%
Difference	+5	+12.9970	+2.6481%	+489000	+14810000	+0.1210	+3.5347%	+13.1180	+3.7648%	+3.7648%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.2714

67.1642%

500000

15000000

0.1230

5.1930%

13.3944

68.8693%

1.7052%

PrimeNet

2⁵⁸

0.0171

62.0690%

10000

180000

0.0018

2.8723%

0.0190

63.1585%

1.0895%

GPU72

2⁶²

0.2744

64.5161%

11000

190000

0.0020

1.6583%

0.2764

65.1046%

0.5884%

Difference

+12.9970

+2.6481%

+489000

+14810000

+0.1210

+3.5347%

+13.1180

+3.7648%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2238947	6071765399115160697	19	62.397	1355942190484 2² × 7 × 79 × 612993757	2009-12-25	79	612993757	0.5481	3.1840	5.9469

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2238947

6071765399115160697

62.397

1355942190484
2² × 7 × 79 × 612993757

2009-12-25

612993757

0.5481

3.1840

5.9469

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.282%
2016-04-22T15:30:29	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.193%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-02-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2022-03-09T16:36:48	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.069	-	-
2009-01-11T05:58:00	Sturle Sunde	goscha.ifi	2⁶⁰	2⁶¹		-	-	0.069	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.965 GHz-days
Estimated T-Level:	0.500

Digits	B1	Curves	Complete	FacMiss
20	11000	10 / 100	0.100	90.438%
25	50000	10 / 280	0.036	96.485%

New Calculation Method

Total ECM effort:	0.965 GHz-days
Estimated T-Level:	0.500

Digits	B1	Complete	FacMiss
20	11000	0.407	66.561%
25	50000	0.038	96.269%
30	250000	0.002	99.759%

ECM Summary

B1	B2	factor	curves	GHz-days
		6071765399115160697	1	0.00000e+0
50000	5000000		3	0.257
50000	7150000		7	0.707

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-28T18:57:00	ksims	ZhViZCJBe1505	50000	5000000						3	0.257
2009-12-25T08:56:00	Dmitry B. Khachaturov	mgp1-1			6071765399115160697	62.397		1		1	-
2022-07-05T13:05:23	debrouxl	athlon2	50000	7150000						7	0.707

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	7839C75D6CAA7AAD	0.147

date

userid

compid

res64

spent (GHz-days)

1999-02-21T00:00:00

ANONYMOUS

v4_computers

7839C75D6CAA7AAD

0.147

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-10T09:24:13

Oliver Kruse

GTX-1

6071765399115160697

81C90497CBBEC1__

2017-11-21T00:17:29

kkmrkkblmbrbk

old

6071765399115160697

81C90497CBBEC1__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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