M2157721 Mersenne number exponent details

Residue

Status

L-L

E2973F4404E77666

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	13.7710	67.1642%	500000	15000000	0.1230	5.1700%	13.8940	68.8618%	1.6976%
PrimeNet	2⁵⁸	0.0178	62.0690%	10000	170000	0.0018	2.8097%	0.0196	63.1347%	1.0657%
GPU72	2⁶²	0.2847	64.5161%	10000	160000	0.0017	1.5189%	0.2865	65.0551%	0.5390%
Difference	+5	+13.4862	+2.6481%	+490000	+14840000	+0.1213	+3.6511%	+13.6075	+3.8067%	+3.8067%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.7710

67.1642%

500000

15000000

0.1230

5.1700%

13.8940

68.8618%

1.6976%

PrimeNet

2⁵⁸

0.0178

62.0690%

10000

170000

0.0018

2.8097%

0.0196

63.1347%

1.0657%

GPU72

2⁶²

0.2847

64.5161%

10000

160000

0.0017

1.5189%

0.2865

65.0551%

0.5390%

Difference

+13.4862

+2.6481%

+490000

+14840000

+0.1213

+3.6511%

+13.6075

+3.8067%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2157721	1155433025185511857	19	60.003	267743842968 2³ × 3 × 7 × 1593713351	2008-12-21	8	1593713351	0.1255	8.2781	15.461

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2157721

1155433025185511857

60.003

267743842968
2³ × 3 × 7 × 1593713351

2008-12-21

1593713351

0.1255

8.2781

15.461

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-03-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.279%
2016-03-29T18:17:05	alpertron	Manual testing	500000	15000000	12	-		-	-	0.123	-	-	5.170%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-01-29T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁸

0.018

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.236 GHz-days
Estimated T-Level:	1.200

Digits	B1	Curves	Complete	FacMiss
20	11000	24 / 100	0.240	78.568%
25	50000	24 / 280	0.086	91.772%

New Calculation Method

Total ECM effort:	2.236 GHz-days
Estimated T-Level:	1.200

Digits	B1	Complete	FacMiss
20	11000	0.968	37.986%
25	50000	0.090	91.416%
30	250000	0.006	99.432%

ECM Summary

B1	B2	factor	curves	GHz-days
		1155433025185511857	1	0.00000e+0
50000	5000000		10	0.854
50000	6750000		7	0.684
50000	7053704		7	0.698

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-21T02:23:00	alan145	Bear4			1155433025185511857	60.003		1		1	-
2018-08-13T23:51:41	ATH	ec2-ECMCF	50000	5000000						3	0.256
2022-02-05T05:28:22	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.598
2022-05-25T20:50:04	Dylan Delgado	colab	50000	6750000						7	0.684
2022-07-25T19:25:24	debrouxl	o9020	50000	7053704						7	0.698

date	userid	compid	res64	spent (GHz-days)
1999-02-07T00:00:00	ANONYMOUS	v4_computers	E2973F4404E77666	0.142

date

userid

compid

res64

spent (GHz-days)

1999-02-07T00:00:00

ANONYMOUS

v4_computers

E2973F4404E77666

0.142

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T23:33:42

Oliver Kruse

GTX-3

1155433025185511857

79914FBD4195E7__

2017-11-18T20:36:59

kkmrkkblmbrbk

c4.xlarge

1155433025185511857

79914FBD4195E7__

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

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