M3126979 Mersenne number exponent details

≡

M3126979

<<<

>>>

is 2 ^3126979 - 1

has 941315 decimal digits

takes 0.266 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- 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	Prob over default TF
Actual	2⁶⁹	38.1796	68.1159%	1200000	236513550	1.7303	7.7191%	39.9099	70.5771%	2.4611%
PrimeNet	2⁶⁰	0.0491	63.3333%	13000	240000	0.0031	2.6463%	0.0522	64.3037%	0.9703%
GPU72	2⁶⁴	1.1383	65.6250%	15000	240000	0.0034	1.5420%	1.1416	66.1551%	0.5301%
Difference	+5	+37.0413	+2.4909%	+1185000	+236273550	+1.7269	+6.1770%	+38.7683	+4.4220%	+1.9311%

Known prime factors (3 factors, 128.8 bits, 0.00411768% 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
3126979	1400886593	10	30.384	224 2⁵ × 7	-	32	32	4.796e-11	3.949e-6	8.037e-6
3126979	21644948639	11	34.333	3461 3461	2008-09-07	1	3461	1.280e-9	2.339e-5	4.346e-5
3126979	18990498166481928001	20	64.042	3036556716000 2⁵ × 3 × 5³ × 179 × 499 × 2833	2017-07-03	499	2833	1.6659	7.728e-5	0.0001

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3126979	1400886593 21644948639	30322118354548696927	20	64.717
3126979	1400886593 18990498166481928001	26603534275815614913392190593	29	94.426
3126979	21644948639 18990498166481928001	411048357442525002903340940639	30	98.375
3126979	1400886593 21644948639 18990498166481928001	575832133015905044634576398649183952927	39	128.759

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-01-03T13:46:11	Jocelyn Larouche	Manual testing	312697	3126979	6	-	skipped known factor: 1400886593 skipped known factor: 21644948639 skipped known factor: 18990498166481928001	-	-	0.058	-	-	2.991%
2022-01-07T14:23:51	Jocelyn Larouche	Manual testing	1050000	116447100		-	skipped known factor: 1400886593 skipped known factor: 21644948639 skipped known factor: 18990498166481928001	-	-	0.905	-	-	6.874%
2022-09-04T10:18:08	Jocelyn Larouche	Manual testing	1200000	236513550		-	skipped known factor: 1400886593 skipped known factor: 21644948639 skipped known factor: 18990498166481928001	-	-	1.730	-	-	7.719%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T19:44:00	Will Edgington	Manual testing	?	?	21644948639	34.333	11	5.48300e-10	0.590	1.21470e-9
2021-01-04T13:51:26	Jocelyn Larouche	Manual testing	2⁶⁰	2⁶¹		-	-	0.049	-	-
2021-01-05T04:03:46	Jocelyn Larouche	Manual testing	2⁶¹	2⁶²		-	-	0.098	-	-
2021-01-06T02:31:36	Jocelyn Larouche	Manual testing	2⁶²	2⁶³		-	-	0.314	-	-
2021-01-09T12:30:22	Jocelyn Larouche	Manual testing	2⁶³	2⁶⁴		-	-	0.628	-	-
2021-01-14T13:16:40	Jocelyn Larouche	Manual testing	2⁶⁴	2⁶⁵	skipped known factors(?)	-	-	1.195	-	-
2017-07-03T10:38:25	TJAOI	Manual testing	2⁶⁴	2⁶⁵*	18990498166481928001	64.042	20	0.528	0.540	1.071
2022-03-20T17:32:05	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	2.390	-	-
2022-03-20T17:32:05	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	4.780	-	-
2021-07-18T23:35:35	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.56	-	-
2021-10-27T11:00:24	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.12	-	-

ECM factoring results:

Total ECM effort:	0.351 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	0.351

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-27T14:34:04	ATH	ec2-ECMCF	50000	5000000						3	0.351

Lucas-Lehmer results:
No L-L results for M3126979

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T13:09:28

alpertron

Manual testing

1400886593

21644948639

18990498166481928001

BA37AF5AFAAEC7__

2017-11-18T08:12:10

Oliver Kruse

Threadripper

1400886593

21644948639

18990498166481928001

BA37AF5AFAAEC7__

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 = 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 = 312697, B2 = 3126979 (P-1 stage 2)

B1 = 312697 (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:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-09-04T10:18:08+00:00

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