M21313 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	1,394.1687	77.6119%	500000000	10000000000	0.4722	13.3953%	1,394.6409	80.6109%	2.9989%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	3.7580%	0.0000	63.9092%	1.4092%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.5893%	0.0001	66.4509%	0.5418%
Difference	+23	+1,394.1686	+11.7028%	+499999500	+9999990000	+0.4722	+11.8060%	+1,394.6408	+14.1600%	+14.1600%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1,394.1687

77.6119%

500000000

10000000000

0.4722

13.3953%

1,394.6409

80.6109%

2.9989%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

3.7580%

0.0000

63.9092%

1.4092%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.5893%

0.0001

66.4509%

0.5418%

Difference

+23

+1,394.1686

+11.7028%

+499999500

+9999990000

+0.4722

+11.8060%

+1,394.6408

+14.1600%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
21313	67988471	8	26.019	1595 5 × 11 × 29	-	11	29	5.643e-10	5.559e-9	1.039e-8
21313	13654429207	11	33.669	320331 3 × 11 × 17 × 571	2008-08-26	17	571	7.172e-8	2.189e-8	2.716e-8
21313	121020179333492177910149432271400524047	39	126.509	2839116486029469758132347212297671 7 × 127 × 971767 × 3286391538226151486241017	2021-10-15	971767	3286391538226151486241017	9.003e+12	8.308e+13	1.552e+14

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

21313

67988471

26.019

1595
5 × 11 × 29

5.643e-10

5.559e-9

1.039e-8

21313

13654429207

33.669

320331
3 × 11 × 17 × 571

2008-08-26

571

7.172e-8

2.189e-8

2.716e-8

21313

121020179333492177910149432271400524047

126.509

2839116486029469758132347212297671
7 × 127 × 971767 × 3286391538226151486241017

2021-10-15

971767

3286391538226151486241017

9.003e+12

8.308e+13

1.552e+14

exponent	prime factors	composite factor	digits	bits*
21313	67988471 13654429207	928343764161672497	18	59.687
21313	67988471 121020179333492177910149432271400524047	8227976953029932266571035281650578658554262137	46	152.527
21313	13654429207 121020179333492177910149432271400524047	1652461471327613387362384629741079666342462640729	49	160.177
21313	67988471 13654429207 121020179333492177910149432271400524047	11234832882197477428589925388999713240381419731778 7035359	57	186.196

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-11-19T00:49:55	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 67988471 skipped known factor: 13654429207	-	-	0.472	-	-	13.395%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-11-19T00:49:55

kkmrkkblmbrbk

Manual testing

500000000

10000000000

skipped known factor: 67988471
skipped known factor: 13654429207

0.472

-

-

13.395%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T19:59:00	ANONYMOUS	Manual testing	?	?	13654429207	33.669	11	1.80251e-8	2.08777e-5	5.51780e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T19:59:00

ANONYMOUS

Manual testing

13654429207

33.669

1.80251e-8

2.08777e-5

5.51780e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.300 GHz-days
Estimated T-Level:	35.426

Digits	B1	Curves	Complete	FacMiss
20	11000	2651 / 100	26.510	0.000%
25	50000	2651 / 280	9.468	0.008%
30	250000	2621 / 640	4.095	1.660%
35	1000000	1712 / 1580	1.084	33.828%
40	3000000	400 / 4700	0.085	91.841%

New Calculation Method

Total ECM effort:	18.300 GHz-days
Estimated T-Level:	35.426

Digits	B1	Complete	FacMiss
20	11000	344.146	0.000%
25	50000	67.573	0.000%
30	250000	10.722	0.002%
35	1000000	1.392	24.866%
40	3000000	0.152	85.862%
45	11000000	0.015	98.543%
50	44000000	0.001	99.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	0.010
250000	25000000		909	1.517
1000000	100000000		1,312	8.760
3000000	300000000		370	7.411
3000000	300000000	121020179333492177910149432271400524047	30	0.601

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-02T14:40:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.010
2009-06-13T08:44:00	unconnected	dual5430	250000	25000000						30	0.050
2011-03-29T06:46:00	James Hintz	17_051310	250000	25000000						11	0.018
2014-10-10T22:46:00	James Hintz	08_04_2014	250000	25000000						434	0.724
2014-10-11T02:36:00	James Hintz	08_04_2014	250000	25000000						434	0.724
2018-02-02T00:05:11	James Hintz	10_12_2017	1000000	100000000						1312	8.760
2021-10-15T21:08:22	nordi	sweet16	3000000	300000000	121020179333492177910149432271400524047	126.509	30	2	1471217152715168	30	0.601
2021-10-18T20:58:54	nordi	sweet16	3000000	300000000						370	7.411

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:26:49

Oliver Kruse

PRP

67988471

13654429207

C643EB452F0A3A__

2017-09-21T21:28:44

Oliver Kruse

Manual testing

67988471

13654429207

C643EB452F0A3A__

2017-10-12T16:29:44

kkmrkkblmbrbk

Manual testing

67988471

13654429207

C643EB452F0A3A__

2020-04-17T13:49:01

Oliver Kruse

Manual testing

67988471

13654429207

F19372E6A694FF__

2021-10-15T21:32:50

SRJ2877

LTOS

67988471

13654429207

121020179333492177910149432271400524047

F19372E6A694FF96

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

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