M3508079 Mersenne number exponent details

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M3508079

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is 2 ^3508079 - 1

has 1056038 decimal digits

takes 0.368 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	2⁶⁸	16.9907	67.6471%	1000000	114656850	1.0953	7.5313%	18.0861	70.0837%	2.4366%
PrimeNet	2⁶⁰	0.0438	63.3333%	15000	300000	0.0046	2.9616%	0.0484	64.4193%	1.0859%
GPU72	2⁶⁴	1.0146	65.6250%	20000	360000	0.0059	1.9162%	1.0205	66.2837%	0.6587%
Difference	+4	+15.9761	+2.0221%	+980000	+114296850	+1.0895	+5.6151%	+17.0656	+3.8000%	+3.8000%

Known prime factors (4 factors, 169.4 bits, 0.00482845% 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
3508079	175403951	9	27.386	25 5²	-	25	25	5.124e-12	3.807e-6	7.748e-6
3508079	22234204703	11	34.372	3169 3169	2008-09-07	1	3169	1.100e-9	2.644e-5	4.904e-5
3508079	1264423930129	13	40.202	180216 2³ × 3² × 2503	2008-09-30	9	2503	4.208e-8	2.206e-5	3.877e-5
3508079	198297198754317669599	21	67.426	28262932327681 6329 × 4465623689	2022-01-26	6329	4465623689	15.665	37.053	69.203

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
3508079	175403951 22234204703	3899967352248981553	19	61.758
3508079	175403951 1264423930129	221784953083574539679	21	67.588
3508079	22234204703 1264423930129	28113460493859955196687	23	74.574
3508079	175403951 198297198754317669599	34782112133739597556777185649	29	94.812
3508079	22234204703 198297198754317669599	4408980509134975670954085924097	31	101.798
3508079	175403951 22234204703 1264423930129	4931212046905447382181881910337	31	101.960
3508079	1264423930129 198297198754317669599	250731723382505790902116083448271	33	107.628
3508079	175403951 22234204703 198297198754317669599	773352601184266324974222610680099907247	39	129.184
3508079	175403951 1264423930129 198297198754317669599	43979334922330600004611015297472437518721	41	135.014
3508079	22234204703 1264423930129 198297198754317669599	5574820463222605324000564035257487525418513	43	142.000
3508079	175403951 22234204703 1264423930129 198297198754317669599	97784553536489516634333405801266661429162010874486 3	51	169.386

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2020-06-15T15:09:18	Jocelyn Larouche	Manual testing	350807	350807		-	skipped known factor: 175403951 skipped known factor: 22234204703 skipped known factor: 1264423930129	-	-	0.053	-	-	1.674%
2020-06-17T04:15:28	Jocelyn Larouche	Manual testing	350807	3508079	6	-	skipped known factor: 175403951 skipped known factor: 22234204703 skipped known factor: 1264423930129	-	-	0.080	-	-	3.520%
2022-02-11T00:02:48	Jocelyn Larouche	Manual testing	1000000	114656850		-	skipped known factor: 175403951 skipped known factor: 22234204703 skipped known factor: 1264423930129	-	-	1.095	-	-	7.531%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T21:28:00	markr	Manual testing	?	?	1264423930129	40.202	13	3.25353e-10	0.792	6.99551e-10
2008-09-07T19:49:00	Will Edgington	Manual testing	?	?	22234204703	34.372	11	4.47501e-10	0.792	9.62187e-10
2022-01-26T20:53:37	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	skipped known factors(?)	-	-	8.521	-	-
2022-01-26T20:53:37	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸	198297198754317669599	67.426	21	7.195	0.748	14.61

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.442 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:	0.442 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	0.442

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-04T10:58:34	rucio		50000	5000000						3	0.442

Lucas-Lehmer results:
No L-L results for M3508079

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-07T13:27:48

kkmrkkblmbrbk

c4.xlarge

175403951

22234204703

1264423930129

EBDC75D8E79A7B__

2017-11-24T06:33:54

Oliver Kruse

GTX-3

175403951

22234204703

1264423930129

EBDC75D8E79A7B__

2022-02-01T23:42:24

Poao

office-CN2

175403951

22234204703

1264423930129

198297198754317669599

EBDC75D8E79A7B31

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 = 1000000, B2 = 114656850 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 350807, B2 = 3508079 (P-1 stage 2)

B1 = 350807 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-11T00:02:48+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