M2100121 Mersenne number exponent details

Residue

Status

L-L

E67B826603CF58E7

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	113.7795	68.5714%	5000000	500000000	3.0478	8.6939%	116.8273	71.3038%	2.7324%
PrimeNet	2⁵⁸	0.0183	62.0690%	9000	160000	0.0016	2.6778%	0.0199	63.0847%	1.0157%
GPU72	2⁶²	0.2925	64.5161%	10000	140000	0.0016	1.4513%	0.2942	65.0311%	0.5150%
Difference	+8	+113.4869	+4.0553%	+4990000	+499860000	+3.0462	+7.2426%	+116.5331	+6.2727%	+2.2174%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷⁰

113.7795

68.5714%

5000000

500000000

3.0478

8.6939%

116.8273

71.3038%

2.7324%

PrimeNet

2⁵⁸

0.0183

62.0690%

9000

160000

0.0016

2.6778%

0.0199

63.0847%

1.0157%

GPU72

2⁶²

0.2925

64.5161%

10000

140000

0.0016

1.4513%

0.2942

65.0311%

0.5150%

Difference

+113.4869

+4.0553%

+4990000

+499860000

+3.0462

+7.2426%

+116.5331

+6.2727%

+2.2174%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2100121	670601135976696343663	21	69.184	159657737810511 3 × 47963 × 1109589599	2014-03-15	47963	1109589599	58.955	5.7678	10.765

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2100121

670601135976696343663

69.184

159657737810511
3 × 47963 × 1109589599

2014-03-15

47963

1109589599

58.955

5.7678

10.765

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.144%
2009-07-15T12:49:00	BigBrother	Miniluv	200000	5000000		-		-	-	0.044	-	-	2.639%
2012-08-22T18:21:00	BloodIce	Mjolnir	5000000	500000000		-		-	-	3.048	-	-	8.694%
2016-03-16T12:12:47	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	3.841%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-01-03T11:50:00	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-02-02T15:33:00	BloodIce	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2012-02-02T15:33:00	BloodIce	Manual testing	2⁶²	2⁶³		-	-	0.467	-	-
2012-02-02T15:33:00	BloodIce	Manual testing	2⁶³	2⁶⁴		-	-	0.935	-	-
2012-02-02T15:33:00	BloodIce	Manual testing	2⁶⁴	2⁶⁵		-	-	1.779	-	-
2012-02-02T15:33:00	BloodIce	Manual testing	2⁶⁵	2⁶⁶		-	-	3.558	-	-
2012-02-04T22:53:00	BloodIce	Manual testing	2⁶⁶	2⁶⁷		-	-	7.116	-	-
2014-03-08T13:51:00	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	14.23	-	-
2014-03-08T13:51:00	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	28.47	-	-
2014-03-08T13:51:00	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰	MISSED FACTOR!	-	-	56.93	-	-

ECM factoring results:

Total ECM effort:	3.270 GHz-days
Estimated T-Level:	20.613

Digits	B1	Complete	FacMiss
20	11000	1.333	26.370%
25	50000	0.123	88.459%
30	250000	0.008	99.232%

ECM Summary

B1	B2	factor	curves	GHz-days
		670601135976696343663	1	0.00000e+0
50000	50000		7	0.355
50000	5000000		12	1.021
50000	5300000		7	0.610
50000	5836236		7	0.636
50000	6056914		7	0.647

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-06T23:59:00	oodaira	Win02	50000	5000000						3	0.255
2009-11-08T23:44:00	James Hintz	ryan	50000	5000000						3	0.255
2011-06-15T18:04:00	S36049	Wolle5	50000	5000000						3	0.255
2013-04-01T19:49:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-03-15T15:05:00	BloodIce	NEDDylator			670601135976696343663	69.184		1		1	-
2022-02-24T07:43:11	JackBlock	school2	50000	50000						7	0.355
2022-03-10T18:21:14	Alex Kruppa	lily	50000	5300000						7	0.610
2022-06-07T10:02:57	debrouxl	o9020	50000	6056914						7	0.647
2022-08-07T23:54:26	debrouxl	dl380g9-1	50000	5836236						7	0.636

date	userid	compid	res64	spent (GHz-days)
1999-04-02T00:00:00	ANONYMOUS	v4_computers	E67B826603CF58E7	0.138

date

userid

compid

res64

spent (GHz-days)

1999-04-02T00:00:00

ANONYMOUS

v4_computers

E67B826603CF58E7

0.138

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07T00:13:45

Oliver Kruse

GTX-0

670601135976696343663

1AE3C8C4904A4F__

2017-11-17T03:10:26

kkmrkkblmbrbk

c4.xlarge

670601135976696343663

1AE3C8C4904A4F__

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 = 5000000, B2 = 500000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 200000, B2 = 5000000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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