M3184471 Mersenne number exponent details

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M3184471

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>>>

is 2 ^3184471 - 1

has 958622 decimal digits

takes 0.271 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	9FD0D9988DD5965D	double-checked
PRP	C182715FB9F1241E	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	18.7174	67.6471%	4000000	150000000	1.4753	8.7569%	20.1927	70.4802%	2.8331%
PrimeNet	2⁶⁰	0.0482	63.3333%	13000	240000	0.0031	2.6551%	0.0514	64.3069%	0.9735%
GPU72	2⁶⁴	1.1177	65.6250%	15000	260000	0.0035	1.5833%	1.1212	66.1693%	0.5443%
Difference	+4	+17.5996	+2.0221%	+3985000	+149740000	+1.4718	+7.1736%	+19.0715	+4.3109%	+4.3109%

Known prime factors (1 factor, 71.6 bits, 0.00224768% 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
3184471	3521715579240019228577	22	71.577	552951428862128 2⁴ × 113 × 305835967291	2021-03-14	113	305835967291	249.86	2,056.4	3,840.7

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-03T07:19:00	Carsten Kossendey	leela	15000	191250		-		-	-	0.003	-	-	0.782%
2011-09-12T19:37:00	Squeeky_Squirrel	T7500_2200	60000	975000		-		-	-	0.014	-	-	1.885%
2014-06-01T23:28:00	Jocelyn Larouche	Manual testing	80155	80155		-		-	-	0.010	-	-	0.753%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	100310	100310		-		-	-	0.012	-	-	0.862%
2015-09-24T01:34:39	Jocelyn Larouche	Manual testing	441191	441191		-		-	-	0.054	-	-	1.826%
2015-11-17T00:21:43	Jocelyn Larouche	Manual testing	558607	558607		-		-	-	0.069	-	-	2.021%
2016-03-08T09:14:06	Jocelyn Larouche	Manual testing	670328	12065904	6	-		-	-	0.159	-	-	4.876%
2019-09-30T10:10:15	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.757%
2022-02-27T01:57:32	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	7.626%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-07-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2009-04-07T22:18:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.048	-	-
2011-10-19T22:39:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:45:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.308	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.617	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.173	-	-
2015-06-18T20:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.347	-	-
2017-05-01T03:37:55	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.693	-	-
2019-01-07T14:44:19	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.386	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.460 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	4.460 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.226	29.352%
25	50000	0.111	89.513%
30	250000	0.007	99.320%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		36	4.225
50000	5000000	3521715579240019228577	2	0.235

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-07T14:08:00	Anu Järvi	Anu	50000	5000000						3	0.352
2011-08-22T02:48:00	sannerud.com	Jim2010	50000	5000000						3	0.352
2014-04-08T17:47:00	Dougal	dougal	50000	5000000						3	0.352
2016-07-10T01:43:12	Dennis Schreiber	z400	50000	5000000						3	0.352
2018-06-03T08:56:25	volki	home	50000	5000000						3	0.352
2020-12-13T04:49:01	daveward2005	Dave2	50000	5000000						7	0.822
2021-01-14T12:39:34	daveward2005	Dave2	50000	5000000						7	0.822
2021-02-13T13:19:18	C.D.B.	i7-6850K	50000	5000000						7	0.822
2021-03-14T16:09:07	daveward2005	Dave2	50000	5000000	3521715579240019228577	71.577	2	2	4596498438416756	2	0.235

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-12T00:00:00	Vassilo	v4_computers	9FD0D9988DD5965D	0.271
1999-06-15T00:00:00	ANONYMOUS	v4_computers	9FD0D9988DD5965D	0.271

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-03-15T14:17:19

happy5214

Focus

3521715579240019228577

C182715FB9F1241E

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 = 670328, B2 = 12065904 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 670328 (P-1 stage 1)

B1 = 558607 (P-1 stage 1)

B1 = 441191 (P-1 stage 1)

B1 = 60000, B2 = 975000 (P-1 stage 2)

B1 = 100310 (P-1 stage 1)

B1 = 80155 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

B1 = 15000, B2 = 191250 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10¹

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10⁵

10⁶

10⁷

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

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-02-27T01:57:32+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