M3274363 Mersenne number exponent details

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M3274363

<<<

>>>

is 2 ^3274363 - 1

has 985682 decimal digits

takes 0.344 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

1 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	DD7AA4C982839B__	unverified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	36.4611	68.1159%	4000000	150000000	1.8206	8.1165%	38.2816	70.7038%	2.5879%
PrimeNet	2⁶⁰	0.0469	63.3333%	14000	260000	0.0042	2.7746%	0.0511	64.3507%	1.0173%
GPU72	2⁶⁴	1.0870	65.6250%	17000	280000	0.0048	1.6867%	1.0918	66.2048%	0.5798%
Difference	+5	+35.3740	+2.4909%	+3983000	+149720000	+1.8158	+6.4298%	+37.1898	+4.4990%	+4.4990%

Known prime factors (1 factor, 75.2 bits, 0.00229772% 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
3274363	44482530590378945870567	23	75.236	6792547220692841 127 × 137 × 193 × 2022791263	2021-10-05	193	2022791263	2,995.0	16.784	31.347

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T04:54:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.671%
2011-09-19T13:51:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.704%
2014-06-26T21:21:00	ANONYMOUS	Manual testing	79602	79602		-		-	-	0.012	-	-	0.651%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99204	99204		-		-	-	0.015	-	-	0.746%
2016-01-17T13:12:28	Jocelyn Larouche	Manual testing	383400	3834000	6	-		-	-	0.087	-	-	3.242%
2016-01-21T11:51:27	Jocelyn Larouche	Manual testing	460080	4600800	6	-		-	-	0.104	-	-	3.457%
2020-12-30T01:44:00	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.117%
2022-04-02T19:48:43	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.015%

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		-	-	0.047	-	-
2009-04-02T04:53:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-10-02T04:42:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.094	-	-
2012-12-30T00:06:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.300	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.600	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.141	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.282	-	-
2017-04-04T13:00:39	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.564	-	-
2018-12-10T15:07:55	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.129	-	-
2021-06-07T10:35:08	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	18.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.879 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	8.879 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	8.297
50000	5000000	44482530590378945870567	4	0.582

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-23T20:17:00	TeamResslerTUB	1062324	50000	5000000						3	0.437
2011-09-22T05:51:00	Smurgs	Praca	50000	5000000						3	0.437
2014-07-04T22:39:00	Bruce	fx6840-21	50000	5000000						3	0.437
2016-09-07T10:51:59	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-01-31T06:16:10	nokno	leo235	50000	5000000						3	0.437
2021-01-21T05:48:25	RIHATEC	i7-3770K	50000	5000000						7	1.019
2021-02-20T05:01:43	mnd9	50869	50000	5000000						7	1.019
2021-03-22T13:58:26	mnd9	office2	50000	5000000						7	1.019
2021-05-07T10:58:30	Zenzoma	AMD3970X	50000	5000000						7	1.019
2021-06-20T00:14:04	daveward2005	Dave2	50000	5000000						7	1.019
2021-08-01T04:58:16	daveward2005	Dave2	50000	5000000						7	1.019
2021-10-05T06:26:52	daveward2005	Dave2	50000	5000000	44482530590378945870567	75.236	4	2	8266587984226219	4	0.582

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	181249167768DA__	0.344

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-10-11T13:54:02

Sébastien Broucke

Portable_Seb

44482530590378945870567

DD7AA4C982839B__

2021-10-14T15:24:48

Peter_Jakub

OptiPlex

44482530590378945870567

DD7AA4C982839B93

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 = 460080, B2 = 4600800 (P-1 stage 2)

B1 = 383400, B2 = 3834000 (P-1 stage 2)

B1 = 460080 (P-1 stage 1)

B1 = 383400 (P-1 stage 1)

B1 = 60000, B2 = 1065000 (P-1 stage 2)

B1 = 99204 (P-1 stage 1)

B1 = 79602 (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

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:43+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