M30781 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	48.8744%	0.3686	48.8744%	48.8744%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1305%	0.0000	64.0489%	1.5489%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7719%	0.0001	66.5132%	0.6041%
Difference	-44	-0.0001	-65.9091%	+199999500	+4999990000	+0.3686	+47.1025%	+0.3685	-17.6387%	-17.6387%

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

48.8744%

0.3686

48.8744%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1305%

0.0000

64.0489%

1.5489%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7719%

0.0001

66.5132%

0.6041%

Difference

-44

-0.0001

-65.9091%

+199999500

+4999990000

+0.3686

+47.1025%

+0.3685

-17.6387%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
30781	184687	6	17.495	3 3	-	1	3	5.676e-13	8.857e-10	1.626e-9
30781	26355250470462033144192728081	29	94.412	428109068426334965468840 2³ × 5 × 23 × 887 × 398759 × 1315626104119	2011-03-17	398759	1315626104119	1.901e+11	57.251	106.93
30781	6793535373218187390955763662567	31	102.422	110352739891786936599781743 3 × 41 × 47 × 149 × 128113201069213004647	2017-07-14	149	128113201069213004647	5.499e+12	5.575e+9	1.041e+10

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

30781

184687

17.495

3
3

5.676e-13

8.857e-10

1.626e-9

30781

26355250470462033144192728081

94.412

428109068426334965468840
2³ × 5 × 23 × 887 × 398759 × 1315626104119

2011-03-17

398759

1315626104119

1.901e+11

57.251

106.93

30781

6793535373218187390955763662567

102.422

110352739891786936599781743
3 × 41 × 47 × 149 × 128113201069213004647

2017-07-14

149

128113201069213004647

5.499e+12

5.575e+9

1.041e+10

exponent	prime factors	composite factor	digits	bits*
30781	184687 26355250470462033144192728081	4867472143638221515301522371095647	34	111.907
30781	184687 6793535373218187390955763662567	1254677667473547374673447123548511529	37	119.917
30781	26355250470462033144192728081 6793535373218187390955763662567	17904532634110909715670748157098825685658408720722 4069443927	60	196.834
30781	184687 26355250470462033144192728081 6793535373218187390955763662567	33067344185960415826580834648901108194071945314040 591713390545849	65	214.329

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-06T09:36:59	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 184687	-	-	0.369	-	-	41.223%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-06T09:36:59

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 184687

0.369

-

-

41.223%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.688 GHz-days
Estimated T-Level:	31.661

Digits	B1	Curves	Complete	FacMiss
20	11000	1346 / 100	13.460	0.000%
25	50000	1346 / 280	4.807	0.810%
30	250000	1109 / 640	1.733	17.655%
35	1000000	525 / 1580	0.332	71.721%
40	3000000	514 / 4700	0.109	89.640%

New Calculation Method

Total ECM effort:	19.688 GHz-days
Estimated T-Level:	31.661

Digits	B1	Complete	FacMiss
20	11000	160.683	0.000%
25	50000	32.518	0.000%
30	250000	5.610	0.366%
35	1000000	0.815	44.265%
40	3000000	0.101	90.400%
45	11000000	0.011	98.917%
50	44000000	0.001	99.896%

ECM Summary

B1	B2	factor	curves	GHz-days
		26355250470462033144192728081	1	0.00000e+0
50000	5000000		237	0.136
250000	25000000		584	1.678
1000000	100000000		11	0.126
3000000	300000000		486	16.76
3000000	300000000	6793535373218187390955763662567	14	0.483
3000000	345407014		7	0.253
3000000	348000000		7	0.254

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30T14:39:00	Matthias Wurtinger	AMD_Funzel	50000	5000000						30	0.017
2010-04-16T07:31:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-16T08:07:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-16T13:16:00	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-21T19:07:00	James Hintz	home2	50000	5000000						174	0.100
2011-01-19T19:15:00	James Hintz	NEW_OMFG	250000	25000000						11	0.032
2011-03-17T14:50:00	James Hintz	17_051310			26355250470462033144192728081	94.412		1		1	-
2014-12-19T04:42:00	James Hintz	08_04_2014	250000	25000000						573	1.646
2014-12-19T05:14:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-07-14T15:24:42	nordi	nordiputer	3000000	300000000	6793535373218187390955763662567	102.422	14	2		14	0.483
2017-07-20T23:21:26	nordi	nordiputer	3000000	300000000						486	16.76
2022-05-15T04:56:15	Luminescence	Tyrant	3000000	345407014						7	0.253
2022-05-15T05:18:25	Luminescence	Tyrant	3000000	348000000						7	0.254

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:41:11

Oliver Kruse

PRP

184687

26355250470462033144192728081

6793535373218187390955763662567

648C38B56A7E05C0

2017-09-21T20:27:23

Oliver Kruse

Manual testing

184687

26355250470462033144192728081

6793535373218187390955763662567

648C38B56A7E05C0

2017-10-02T10:35:42

kkmrkkblmbrbk

Manual testing

184687

26355250470462033144192728081

6793535373218187390955763662567

648C38B56A7E05__

2017-12-07T03:12:41

ATH

xps

184687

26355250470462033144192728081

6793535373218187390955763662567

648C38B56A7E05__

2020-04-17T13:47:28

Oliver Kruse

Manual testing

184687

26355250470462033144192728081

6793535373218187390955763662567

D6C1BD7D24CDAC__

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)

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

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