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
Actual	2⁷⁰	113.7795	68.5714%	5000000	500000000	3.0478	8.6939%	116.8273	71.3038%
Target	2⁶²	0.2925	64.5161%	10000	140000	0.0016	1.4513%	0.2942	65.0311%
Difference	+8	+113.4869	+4.0553%	+4990000	+499860000	+3.0462	+7.2426%	+116.5331	+6.2727%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Actual

2⁷⁰

113.7795

68.5714%

5000000

500000000

3.0478

8.6939%

116.8273

71.3038%

Target

2⁶²

0.2925

64.5161%

10000

140000

0.0016

1.4513%

0.2942

65.0311%

Difference

+113.4869

+4.0553%

+4990000

+499860000

+3.0462

+7.2426%

+116.5331

+6.2727%

	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
2003-02-27	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.144%
2009-07-15	BigBrother	Miniluv	200000	5000000		-		-	-	0.044	-	-	2.639%
2012-08-22	BloodIce	Mjolnir	5000000	500000000		-		-	-	3.048	-	-	8.694%
2016-03-16	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
2009-01-03	Sturle Sunde	othello.ifi	2⁶⁰	2⁶¹		-	-	0.073	-	-
2012-02-02	BloodIce	Manual testing	2⁶¹	2⁶²		-	-	0.146	-	-
2012-02-02	BloodIce	Manual testing	2⁶²	2⁶³		-	-	0.467	-	-
2012-02-02	BloodIce	Manual testing	2⁶³	2⁶⁴		-	-	0.935	-	-
2012-02-02	BloodIce	Manual testing	2⁶⁴	2⁶⁵		-	-	1.779	-	-
2012-02-02	BloodIce	Manual testing	2⁶⁵	2⁶⁶		-	-	3.558	-	-
2012-02-04	BloodIce	Manual testing	2⁶⁶	2⁶⁷		-	-	7.116	-	-
2014-03-08	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	14.23	-	-
2014-03-08	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	28.47	-	-
2014-03-08	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰	MISSED FACTOR!	-	-	56.93	-	-

ECM factoring results:

Total ECM effort:	5.811 GHz-days
Estimated T-Level:	20.782

Digits	B1	Complete	FacMiss
20	11000	1.683	18.583%
25	50000	0.156	85.517%
30	250000	0.010	99.015%

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
50000	45039225		7	2.541

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-06	oodaira	Win02	50000	5000000						3	0.255
2009-11-08	James Hintz	ryan	50000	5000000						3	0.255
2011-06-15	S36049	Wolle5	50000	5000000						3	0.255
2013-04-01	Donna Noble	CCI_PH2_955	50000	5000000						3	0.255
2014-03-15	BloodIce	NEDDylator			670601135976696343663	69.184		1		1	-
2022-02-24	JackBlock	school2	50000	50000						7	0.355
2022-03-10	Alex Kruppa	lily	50000	5300000						7	0.610
2022-06-07	debrouxl	o9020	50000	6056914						7	0.647
2022-08-07	debrouxl	dl380g9-1	50000	5836236						7	0.636
2022-10-11	Stef42	AMD-DESKTOP	50000	45039225						7	2.541

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

date

userid

compid

res64

spent (GHz-days)

1999-04-02

ANONYMOUS

v4_computers

E67B826603CF58E7

0.138

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-07

Oliver Kruse

GTX-0

670601135976696343663

1AE3C8C4904A4F__

2017-11-17

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