M2129051 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	13.9564	67.1642%	500000	15000000	0.1230	5.1617%	14.0794	68.8591%	1.6949%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	160000	0.0016	2.6847%	0.0197	63.0873%	1.0183%
GPU72	2⁶²	0.2886	64.5161%	10000	140000	0.0016	1.4554%	0.2902	65.0326%	0.5164%
Difference	+5	+13.6679	+2.6481%	+490000	+14860000	+0.1214	+3.7063%	+13.7892	+3.8265%	+3.8265%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

13.9564

67.1642%

500000

15000000

0.1230

5.1617%

14.0794

68.8591%

1.6949%

PrimeNet

2⁵⁸

0.0180

62.0690%

9000

160000

0.0016

2.6847%

0.0197

63.0873%

1.0183%

GPU72

2⁶²

0.2886

64.5161%

10000

140000

0.0016

1.4554%

0.2902

65.0326%

0.5164%

Difference

+13.6679

+2.6481%

+490000

+14860000

+0.1214

+3.7063%

+13.7892

+3.8265%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2129051	4258103	7	22.022	1 1	-	1	1	2.625e-13	9.534e-8	1.940e-7
2129051	17032409	8	24.022	4 2²	2008-07-14	4	4	1.051e-12	3.813e-7	7.761e-7
2129051	9606278113	10	33.161	2256 2⁴ × 3 × 47	2008-07-14	16	47	7.999e-10	1.686e-6	3.104e-6
2129051	204928843532264517569	21	67.474	48126804743584 2⁵ × 7 × 59 × 3641556049	2019-10-14	59	3641556049	25.273	18.915	35.328

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2129051

4258103

22.022

1
1

2.625e-13

9.534e-8

1.940e-7

2129051

17032409

24.022

4
2²

2008-07-14

1.051e-12

3.813e-7

7.761e-7

2129051

9606278113

33.161

2256
2⁴ × 3 × 47

2008-07-14

7.999e-10

1.686e-6

3.104e-6

2129051

204928843532264517569

67.474

48126804743584
2⁵ × 7 × 59 × 3641556049

2019-10-14

3641556049

25.273

18.915

35.328

exponent	prime factors	composite factor	digits	bits*
2129051	4258103 17032409	72525751860127	14	46.044
2129051	4258103 9606278113	40904521651799639	17	55.183
2129051	17032409 9606278113	163618057788364217	18	57.183
2129051	4258103 17032409 9606278113	696702542722807037500351	24	79.205
2129051	4258103 204928843532264517569	872608123431266139054111607	27	89.495
2129051	17032409 204928843532264517569	3490431878938533959422893721	28	91.495
2129051	9606278113 204928843532264517569	1968603464346394244449588667297	31	100.635
2129051	4258103 17032409 204928843532264517569	14862618455003808268220502022071263	35	113.517
2129051	4258103 9606278113 204928843532264517569	8382516317343774371473526852983357591	37	122.657
2129051	17032409 9606278113 204928843532264517569	33530059363564704446711374063167428473	38	124.657
2129051	4258103 17032409 9606278113 204928843532264517569	142774446366172958698655042032495416683166719	45	146.679

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T11:24:12	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 4258103 skipped known factor: 17032409 skipped known factor: 9606278113	-	-	0.123	-	-	5.162%

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.837 GHz-days
Estimated T-Level:	1.000

Digits	B1	Curves	Complete	FacMiss
20	11000	20 / 100	0.200	81.791%
25	50000	20 / 280	0.071	93.094%

New Calculation Method

Total ECM effort:	1.837 GHz-days
Estimated T-Level:	1.000

Digits	B1	Complete	FacMiss
20	11000	0.668	51.260%
25	50000	0.060	94.160%
30	250000	0.004	99.629%

ECM Summary

B1	B2	factor	curves	GHz-days
		17032409	1	0.00000e+0
		9606278113	1	0.00000e+0
50000	5000000		3	0.256
50000	5000000	204928843532264517569	3	0.256
50000	5946958		7	0.643
50000	6750000		7	0.682

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-07-14T20:20:00	George Woltman	Manual testing			9606278113	33.161		1		1	-
2008-07-14T20:20:00	George Woltman	Manual testing			17032409	24.022		1		1	-
2018-01-08T02:04:26	ATH	ec2-1xd	50000	5000000						3	0.256
2019-10-14T04:08:12	mnd9	dlounge	50000	5000000	204928843532264517569	67.474	3	2	577811318047467	3	0.256
2021-12-23T15:05:38	Dylan Delgado	colab	50000	6750000						7	0.682
2022-05-16T17:20:17	debrouxl	dl380g9-1	50000	5946958						7	0.643

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-08T12:39:22

Oliver Kruse

GTX-3

4258103

17032409

9606278113

7035C93AB564F1__

2017-11-18T05:44:11

kkmrkkblmbrbk

old

4258103

17032409

9606278113

7035C93AB564F1__

2019-10-15T01:43:58

mnd9

27016b

4258103

17032409

9606278113

204928843532264517569

6031C6795B26A69E

2019-10-15T02:56:48

Jaytholomew

4258103

17032409

9606278113

204928843532264517569

6031C6795B26A69E

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)

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