M30941 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	unknown	200000000	5000000000	0.3686	48.8833%	0.3686	48.8833%	48.8833%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1359%	0.0000	64.0510%	1.5510%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7746%	0.0001	66.5141%	0.6050%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1087%	+0.3685	-17.6308%	-17.6308%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

200000000

5000000000

0.3686

48.8833%

0.3686

48.8833%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1359%

0.0000

64.0510%

1.5510%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7746%

0.0001

66.5141%

0.6050%

Difference

-44

-0.0001

-65.9091%

+199999500

+4999990000

+0.3686

+47.1087%

+0.3685

-17.6308%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
30941	29881270751	11	34.799	482875 5³ × 3863	-	125	3863	1.123e-7	2.625e-7	3.139e-7
30941	359967472893325370087089	24	78.252	5816998042941814584 2³ × 3 × 97 × 344797 × 7246903249	2010-04-22	344797	7246903249	2,476,970	0.3156	0.5890
30941	536027981952720885801147535421911	33	108.724	8662098541623103419429681255 3 × 5 × 7 × 157 × 25643 × 20491102993277041681	2017-06-29	25643	20491102993277041681	4.291e+12	891,687,423	1.665e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

30941

29881270751

34.799

482875
5³ × 3863

125

3863

1.123e-7

2.625e-7

3.139e-7

30941

359967472893325370087089

78.252

5816998042941814584
2³ × 3 × 97 × 344797 × 7246903249

2010-04-22

344797

7246903249

2,476,970

0.3156

0.5890

30941

536027981952720885801147535421911

108.724

8662098541623103419429681255
3 × 5 × 7 × 157 × 25643 × 20491102993277041681

2017-06-29

25643

20491102993277041681

4.291e+12

891,687,423

1.665e+9

exponent	prime factors	composite factor	digits	bits*
30941	29881270751 359967472893325370087089	10756285519078708724309582858433839	35	113.051
30941	29881270751 536027981952720885801147535421911	16017197258841394469756641052438485608825161	44	143.523
30941	359967472893325370087089 536027981952720885801147535421911	19295263806362995613838962176017413380789488789442 8807079	57	186.976
30941	29881270751 359967472893325370087089 536027981952720885801147535421911	57656700200990350852454747129442444812206097665222 19488821544446329	67	221.775

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-06T09:37:00	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 29881270751	-	-	0.369	-	-	41.233%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-06T09:37:00

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 29881270751

0.369

-

-

41.233%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.179 GHz-days
Estimated T-Level:	34.782

Digits	B1	Curves	Complete	FacMiss
20	11000	2326 / 100	23.260	0.000%
25	50000	2326 / 280	8.307	0.024%
30	250000	2096 / 640	3.275	3.772%
35	1000000	1511 / 1580	0.956	38.418%

New Calculation Method

Total ECM effort:	19.179 GHz-days
Estimated T-Level:	34.782

Digits	B1	Complete	FacMiss
20	11000	272.026	0.000%
25	50000	50.890	0.000%
30	250000	7.518	0.054%
35	1000000	0.888	41.159%
40	3000000	0.086	91.742%
45	11000000	0.007	99.282%

ECM Summary

B1	B2	factor	curves	GHz-days
		359967472893325370087089	1	0.00000e+0
50000	5000000		230	0.132
250000	25000000		585	1.681
1000000	100000000		697	8.011
1000000	100000000	536027981952720885801147535421911	814	9.355

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-31T12:34:00	Matthias Wurtinger	AMD_Funzel	50000	5000000						30	0.017
2010-04-13T17:36:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T17:54:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13T23:14:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T04:33:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T17:11:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14T23:28:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T04:37:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15T09:44:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-22T10:45:00	James Hintz	home2			359967472893325370087089	78.252		1		1	-
2010-04-26T17:28:00	James Hintz	04_122109	50000	5000000						112	0.064
2011-01-20T00:19:00	James Hintz	NEW_OMFG	250000	25000000						11	0.032
2011-03-17T09:11:00	James Hintz	17_051310	250000	25000000						11	0.032
2015-05-13T20:42:00	James Hintz	08_04_2014	250000	25000000						563	1.618
2015-05-13T22:00:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-06-29T22:01:29	nordi	nordiputer	1000000	100000000	536027981952720885801147535421911	108.724	814	2		814	9.355
2017-07-02T22:29:04	nordi	nordiputer	1000000	100000000						686	7.884

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:12

Oliver Kruse

Ollaptop

D5B48219101902__

2017-09-21T21:38:48

Oliver Kruse

Manual testing

D5B48219101902__

2017-10-02T10:35:42

kkmrkkblmbrbk

Manual testing

29881270751

359967472893325370087089

536027981952720885801147535421911

D5B48219101902__

2017-12-07T03:12:44

ATH

xps

29881270751

359967472893325370087089

536027981952720885801147535421911

D5B48219101902__

2020-04-17T13:47:31

Oliver Kruse

Manual testing

29881270751

359967472893325370087089

536027981952720885801147535421911

0DB4E5F2E0DAF9__

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 = 200000000, B2 = 5000000000 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

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