M3307277 Mersenne number exponent details

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M3307277

<<<

>>>

is 2 ^3307277 - 1

has 995590 decimal digits

takes 0.347 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	D0F4CF09B7CBC2EC	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	18.0223	67.6471%	4000000	150000000	1.8206	8.7882%	19.8429	70.4903%	2.8433%
PrimeNet	2⁶⁰	0.0464	63.3333%	14000	260000	0.0042	2.7795%	0.0506	64.3525%	1.0192%
GPU72	2⁶⁴	1.0762	65.6250%	17000	300000	0.0049	1.7229%	1.0811	66.2172%	0.5922%
Difference	+4	+16.9461	+2.0221%	+3983000	+149700000	+1.8156	+7.0654%	+18.7617	+4.2731%	+4.2731%

Known prime factors (1 factor, 68.2 bits, 0.00206249% 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
3307277	341904426562385233201	21	68.212	51689717335800 2³ × 3³ × 5² × 23 × 416181299	2021-05-23	27	416181299	28.586	3.4531	6.4495

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T00:40:00	Carsten Kossendey	durandal	15000	195000		-		-	-	0.004	-	-	0.793%
2011-09-30T11:51:00	harlee	P4_2600	55000	880000		-		-	-	0.015	-	-	1.810%
2012-11-15T20:27:00	Squeeky_Squirrel	P4_2600	205000	4612500		-		-	-	0.068	-	-	3.455%
2018-08-06T19:37:31	Jocelyn Larouche	low 4M	410000	820000		-		-	-	0.066	-	-	2.340%
2018-08-07T17:09:32	Jocelyn Larouche	low 4M	410000	1230000		-		-	-	0.069	-	-	2.673%
2018-08-08T12:55:45	Jocelyn Larouche	low 4M	410000	1640000		-		-	-	0.073	-	-	2.912%
2018-08-08T23:04:25	Jocelyn Larouche	low 4M	410000	2050000		-		-	-	0.076	-	-	3.099%
2018-08-13T04:30:29	Jocelyn Larouche	low 4M	410000	4100000		-		-	-	0.093	-	-	3.687%
2020-02-09T13:35:07	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.788%
2022-04-02T19:48:48	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.657%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.046	-	-
2009-04-01T04:45:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.046	-	-
2011-09-07T20:51:00	markr	Manual testing	2¹	2⁶²		-	-	0.186	-	-
2012-08-25T21:54:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.483	-	-
2016-02-23T16:29:25	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.297	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.594	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.130	-	-
2016-02-29T17:40:41	Yxinity	Manual testing	2⁶⁵	2⁶⁶		-	-	2.259	-	-
2017-02-24T15:45:24	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.519	-	-
2018-12-03T19:08:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.038	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.979 GHz-days
Estimated T-Level:	2.050

Digits	B1	Curves	Complete	FacMiss
20	11000	41 / 100	0.410	66.228%
25	50000	41 / 280	0.146	86.356%

New Calculation Method

Total ECM effort:	5.979 GHz-days
Estimated T-Level:	2.050

Digits	B1	Complete	FacMiss
20	11000	1.323	26.645%
25	50000	0.120	88.733%
30	250000	0.007	99.267%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	5.250
50000	5000000	341904426562385233201	5	0.729

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-02T10:32:00	linded	KCPB8M6-SH210	50000	5000000						3	0.437
2011-10-23T13:36:00	Pool Party	desk_2	50000	5000000						3	0.437
2014-07-24T05:43:00	Travis Glenn Russo	i5-spare	50000	5000000						3	0.437
2016-09-25T16:25:31	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-03-01T14:16:25	Idgo	Pentium_Desktop	50000	5000000						3	0.437
2021-01-27T07:39:11	GAN	KL-SCH01	50000	5000000						7	1.021
2021-02-25T10:26:53	Zenzoma	AMD3970X	50000	5000000						7	1.021
2021-03-31T10:39:09	Zenzoma	AMD3970X	50000	5000000						7	1.021
2021-05-23T06:00:41	daveward2005	d12436	50000	5000000	341904426562385233201	68.212	5	2	2310345039061476	5	0.729

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	5068E9E9D251CB__	0.347

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-23T19:32:43

tottenhoff

2018pc

341904426562385233201

D0F4CF09B7CBC2EC

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134316000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 410000, B2 = 4100000 (P-1 stage 2)

B1 = 410000, B2 = 2050000 (P-1 stage 2)

B1 = 410000, B2 = 1640000 (P-1 stage 2)

B1 = 410000, B2 = 1230000 (P-1 stage 2)

B1 = 205000, B2 = 4612500 (P-1 stage 2)

B1 = 410000, B2 = 820000 (P-1 stage 2)

B1 = 410000 (P-1 stage 1)

B1 = 205000 (P-1 stage 1)

B1 = 55000, B2 = 880000 (P-1 stage 2)

B1 = 55000 (P-1 stage 1)

B1 = 15000, B2 = 195000 (P-1 stage 2)

B1 = 15000 (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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:48+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