M3193339 Mersenne number exponent details

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M3193339

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>>>

is 2 ^3193339 - 1

has 961291 decimal digits

takes 0.272 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	F78208A0A7974BF0	double-checked
PRP	D6ABBD58EFBDDFEC	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	18.6654	67.6471%	4000000	150000000	1.4753	8.7592%	20.1407	70.4809%	2.8339%
PrimeNet	2⁶⁰	0.0481	63.3333%	13000	240000	0.0031	2.6564%	0.0512	64.3074%	0.9740%
GPU72	2⁶⁴	1.1146	65.6250%	16000	260000	0.0036	1.6151%	1.1182	66.1802%	0.5552%
Difference	+4	+17.5508	+2.0221%	+3984000	+149740000	+1.4717	+7.1441%	+19.0225	+4.3007%	+4.3007%

Known prime factors (1 factor, 74.7 bits, 0.00233848% 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
3193339	30167959480165207064737	23	74.675	4723576087625712 2⁴ × 3³ × 89 × 122856223669	2021-01-19	89	122856223669	1,979.2	826.06	1,542.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.252%
2013-01-09T14:54:00	Squeeky_Squirrel	T7500_2200	215000	6235000		-		-	-	0.067	-	-	3.690%
2018-09-04T00:51:12	Jocelyn Larouche	low 4M	520300	1040600		-		-	-	0.068	-	-	2.556%
2018-09-04T09:57:13	Jocelyn Larouche	low 4M	520300	1560900		-		-	-	0.071	-	-	2.908%
2018-09-04T22:49:14	Jocelyn Larouche	low 4M	520300	2081200		-		-	-	0.075	-	-	3.160%
2018-09-05T02:02:13	Jocelyn Larouche	low 4M	520300	2601500		-		-	-	0.078	-	-	3.357%
2018-09-05T10:15:26	Jocelyn Larouche	low 4M	520300	3121800		-		-	-	0.082	-	-	3.519%
2018-09-05T21:49:52	Jocelyn Larouche	low 4M	520300	3642100		-		-	-	0.085	-	-	3.656%
2018-09-06T23:06:13	Jocelyn Larouche	low 4M	520300	4162400		-		-	-	0.089	-	-	3.775%
2019-11-10T04:52:10	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.759%
2022-02-27T01:57:43	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.629%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-07T05:39:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-18T04:30:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.307	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.615	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.170	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.340	-	-
2017-05-01T03:37:58	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.680	-	-
2018-12-24T09:14:05	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.360	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.814 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:	4.814 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		22	2.583
50000	5000000	30167959480165207064737	19	2.231

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-17T21:23:00	Lehaleb	Lehaleb01	50000	5000000						3	0.352
2011-08-26T02:29:00	sannerud.com	Jens2010	50000	5000000						3	0.352
2014-04-21T01:19:00	Dougal	dougal	50000	5000000						3	0.352
2016-07-16T01:15:41	Dennis Schreiber	z400	50000	5000000						3	0.352
2018-07-15T15:33:29	IanGlencross	glenx24	50000	5000000						3	0.352
2020-12-18T12:08:08	daveward2005	Dave2	50000	5000000						7	0.822
2021-01-19T19:44:28	MarkS	desktop-i7	50000	5000000	30167959480165207064737	74.675	19	2	379718599432638	19	2.231

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-06-28T00:00:00	ANONYMOUS	v4_computers	F78208A0A7974BF0	0.272
1999-05-30T00:00:00	Dry Creek Photo	v4_computers	F78208A0A7974BF0	0.272

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-01-19T21:24:45

MarkS

desktop-i7

30167959480165207064737

D6ABBD58EFBDDFEC

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 = 134343300 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 520300, B2 = 4162400 (P-1 stage 2)

B1 = 520300, B2 = 3642100 (P-1 stage 2)

B1 = 520300, B2 = 3121800 (P-1 stage 2)

B1 = 520300, B2 = 2601500 (P-1 stage 2)

B1 = 520300, B2 = 2081200 (P-1 stage 2)

B1 = 520300, B2 = 1560900 (P-1 stage 2)

B1 = 520300, B2 = 1040600 (P-1 stage 2)

B1 = 215000, B2 = 6235000 (P-1 stage 2)

B1 = 520300 (P-1 stage 1)

B1 = 215000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-27T01:57:43+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