M3102929 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	2⁶⁸	19.2092	67.6471%	1050000	116447100	0.9055	7.4901%	20.1147	70.0703%	2.4233%
PrimeNet	2⁶⁰	0.0495	63.3333%	12000	220000	0.0029	2.5308%	0.0524	64.2613%	0.9280%
GPU72	2⁶⁴	1.1471	65.6250%	14000	240000	0.0032	1.5074%	1.1503	66.1432%	0.5182%
Difference	+4	+18.0621	+2.0221%	+1036000	+116207100	+0.9022	+5.9827%	+18.9644	+3.9272%	+3.9272%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.2092

67.6471%

1050000

116447100

0.9055

7.4901%

20.1147

70.0703%

2.4233%

PrimeNet

2⁶⁰

0.0495

63.3333%

12000

220000

0.0029

2.5308%

0.0524

64.2613%

0.9280%

GPU72

2⁶⁴

1.1471

65.6250%

14000

240000

0.0032

1.5074%

1.1503

66.1432%

0.5182%

Difference

+18.0621

+2.0221%

+1036000

+116207100

+0.9022

+5.9827%

+18.9644

+3.9272%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3102929	43441007	8	25.373	7 7	-	1	7	1.443e-12	1.638e-7	2.512e-7
3102929	754979860849	12	39.458	121656 2³ × 3 × 37 × 137	2008-09-30	37	137	3.145e-8	5.239e-6	9.293e-6
3102929	20053933871452914817	20	64.121	3231452261952 2⁶ × 3² × 1213 × 4625029	2017-07-24	1213	4625029	1.8070	0.0312	0.0581

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3102929

43441007

25.373

7
7

1.443e-12

1.638e-7

2.512e-7

3102929

754979860849

39.458

121656
2³ × 3 × 37 × 137

2008-09-30

137

3.145e-8

5.239e-6

9.293e-6

3102929

20053933871452914817

64.121

3231452261952
2⁶ × 3² × 1213 × 4625029

2017-07-24

1213

4625029

1.8070

0.0312

0.0581

exponent	prime factors	composite factor	digits	bits*
3102929	43441007 754979860849	32797085420000434943	20	64.830
3102929	43441007 20053933871452914817	871163081687323172735700719	27	89.493
3102929	754979860849 20053933871452914817	15140316203744569481994110299633	32	103.578
3102929	43441007 754979860849 20053933871452914817	657710582189081269079292519485129250431	39	128.951

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-23T16:42:53	Jocelyn Larouche	Manual testing	310292	3102929	6	-	skipped known factor: 43441007 skipped known factor: 754979860849	-	-	0.057	-	-	3.315%
2022-01-07T23:58:00	Jocelyn Larouche	Manual testing	1050000	116447100		-	skipped known factor: 43441007 skipped known factor: 754979860849 skipped known factor: 20053933871452914817	-	-	0.905	-	-	7.490%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T14:46:00	markr	Manual testing	?	?	754979860849	39.458	12	7.84713e-9	0.586	1.74089e-8
2021-01-04T09:13:17	Jocelyn Larouche	Manual testing	2⁵⁹	2⁶⁰		-	-	0.025	-	-
2021-01-04T13:51:26	Jocelyn Larouche	Manual testing	2⁶⁰	2⁶¹		-	-	0.049	-	-
2021-01-05T04:03:47	Jocelyn Larouche	Manual testing	2⁶¹	2⁶²		-	-	0.099	-	-
2021-01-05T18:32:51	Jocelyn Larouche	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2021-01-07T23:43:18	Jocelyn Larouche	Manual testing	2⁶³	2⁶⁴		-	-	0.633	-	-
2021-01-11T11:48:23	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵	skipped known factors(?)	-	-	1.204	-	-
2022-01-18T23:14:39	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵	20053933871452914817	64.121	20	0.660	0.536	1.340
2017-07-24T11:15:18	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	20053933871452914817	64.121	20	0.660	0.536	1.340
2022-03-16T23:46:19	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.408	-	-
2022-03-16T23:46:19	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.817	-	-
2021-06-23T17:43:47	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.63	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.097	90.776%
25	50000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.350

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-17T21:33:19	Dt12	Core_i5-8250U	50000	5000000						3	0.350

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:49

alpertron

Manual testing

43441007

754979860849

20053933871452914817

5763D76730C4F4__

2017-11-18T05:25:44

Oliver Kruse

Threadripper

43441007

754979860849

20053933871452914817

5763D76730C4F4__

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 = 1050000, B2 = 116447100 (P-1 stage 2)

B1 = 1050000 (P-1 stage 1)

B1 = 310292, B2 = 3102929 (P-1 stage 2)

B1 = 310292 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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