M3 102 929 Mersenne number exponent details

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M3102929

<<<

>>>

is 2 ^3102929 - 1

has 934075 decimal digits

takes 0.264 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	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
Actual	2⁶⁸	19.2092	67.6471%	1200000	451528350	3.1760	9.1137%	22.3852	70.5956%
Target	2⁶⁴	1.1471	65.6250%	14000	1920000	0.0145	1.5074%	1.1616	66.1432%
Difference	+4	+18.0621	+2.0221%	+1186000	+449608350	+3.1615	+7.6063%	+21.2236	+4.4524%

Known prime factors (3 factors, 129.0 bits, 0.00415577% known):

Remaining cofactor is not a probable-prime

						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

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

4 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-12-23	Jocelyn Larouche	Manual testing	310292	3102929	6	-	skipped known factor: 43441007 skipped known factor: 754979860849	-	-	0.057	-	-	3.315%
2022-01-07	Jocelyn Larouche	Manual testing	1050000	116447100		-	skipped known factor: 43441007 skipped known factor: 754979860849 skipped known factor: 20053933871452914817	-	-	0.905	-	-	7.490%
2022-09-04	Jocelyn Larouche	Manual testing	1200000	236513550		-	skipped known factor: 43441007 skipped known factor: 754979860849 skipped known factor: 20053933871452914817	-	-	1.730	-	-	8.387%
2022-10-07	Jocelyn Larouche	Manual testing	1200000	451528350		-	skipped known factor: 43441007 skipped known factor: 754979860849 skipped known factor: 20053933871452914817	-	-	3.176	-	-	9.114%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30	markr	Manual testing	?	?	754979860849	39.458	12	7.84713e-9	1.679	4.98746e-8
2021-01-04	Jocelyn Larouche	Manual testing	2⁵⁹	2⁶⁰		-	-	0.025	-	-
2021-01-04	Jocelyn Larouche	Manual testing	2⁶⁰	2⁶¹		-	-	0.049	-	-
2021-01-05	Jocelyn Larouche	Manual testing	2⁶¹	2⁶²		-	-	0.099	-	-
2021-01-05	Jocelyn Larouche	Manual testing	2⁶²	2⁶³		-	-	0.316	-	-
2021-01-07	Jocelyn Larouche	Manual testing	2⁶³	2⁶⁴		-	-	0.633	-	-
2017-07-24	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	20053933871452914817	64.121	20	0.660	0.531	1.328
2021-01-11	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵	skipped known factors(?)	-	-	1.204	-	-
2022-01-18	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵	20053933871452914817	64.121	20	0.660	0.531	1.328
2022-03-16	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.408	-	-
2022-03-16	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.817	-	-
2021-06-23	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.63	-	-

ECM factoring results:

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

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
2018-07-17	Dt12	Core_i5-8250U	50000	5000000						3	0.350

Lucas-Lehmer results:
No L-L results for M3102929

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28

alpertron

Manual testing

43441007

754979860849

20053933871452914817

5763D76730C4F4__

2017-11-18

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 = 1200000, B2 = 451528350 (P-1 stage 2)

B1 = 1200000, B2 = 236513550 (P-1 stage 2)

B1 = 1050000, B2 = 116447100 (P-1 stage 2)

B1 = 1200000 (P-1 stage 1)

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

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

this exponent TF target: 64

TF double-checked to: 67.9

ECM T-Level=0.58 ~= -15-bit

2⁵⁰

2⁶⁰

2⁷⁰

Last modified: 2023-07-11T14:45:05+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
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50M	<	146M	PrimeNet wavefront