M3261451 Mersenne number exponent details

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M3261451

<<<

>>>

is 2 ^3261451 - 1

has 981795 decimal digits

takes 0.343 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	4E4CD18B76E4A395	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	2⁶⁹	36.6054	68.1159%	10000000	400000000	4.7588	9.9064%	41.3642	71.2745%	3.1586%
PrimeNet	2⁶⁰	0.0471	63.3333%	14000	260000	0.0042	2.7726%	0.0513	64.3500%	1.0166%
GPU72	2⁶⁴	1.0913	65.6250%	17000	280000	0.0048	1.6855%	1.0961	66.2044%	0.5794%
Difference	+5	+35.5141	+2.4909%	+9983000	+399720000	+4.7540	+8.2209%	+40.2681	+5.0701%	+5.0701%

Known prime factors (1 factor, 74.7 bits, 0.00228941% 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
3261451	30009676728507436540631	23	74.668	4600663436076065 5 × 937 × 981998598949	2021-06-21	937	981998598949	1,479.0	8,147.8	15,218

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-06T04:16:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.670%
2011-09-15T06:13:00	harlee	P4_2600	60000	1050000		-		-	-	0.017	-	-	1.696%
2014-06-13T02:40:00	Jocelyn Larouche	Manual testing	79680	79680		-		-	-	0.012	-	-	0.651%
2014-10-07T22:12:00	Jocelyn Larouche	Manual testing	99360	99360		-		-	-	0.015	-	-	0.746%
2016-01-20T03:06:56	Jocelyn Larouche	Manual testing	415800	4158000	6	-		-	-	0.094	-	-	3.335%
2020-09-26T11:16:24	mikr	MSI	4000000	150000000	12	-		-	-	1.821	-	-	8.113%
2021-01-29T03:06:06	axn	Manual testing	10000000	400000000		-		-	-	4.759	-	-	9.906%
2022-04-02T19:48:45	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.012%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-03T10:32:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-09-25T01:24:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.094	-	-
2012-12-30T00:02:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.301	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.602	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.146	-	-
2015-06-28T13:57:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.291	-	-
2017-04-04T13:00:34	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.582	-	-
2019-01-07T14:44:12	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.165	-	-
2021-02-08T00:20:52	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.33	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.238 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	7.238 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.398	24.700%
25	50000	0.136	87.309%
30	250000	0.009	99.079%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.182
50000	5000000	30009676728507436540631	3	0.436
50000	6350000		3	0.489
80000	11280000		15	4.131

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-20T08:57:00	James Hintz	13_060209	50000	5000000						3	0.436
2011-09-19T07:22:00	Pool Party	desk_1	50000	5000000						3	0.436
2014-06-24T10:38:00	arnaud	Chamot18	50000	5000000						3	0.436
2016-09-01T06:36:22	Dennis Schreiber	z400	50000	5000000						3	0.436
2018-12-30T16:20:22	IanGlencross	glenx24	50000	5000000						3	0.436
2020-12-30T07:12:47	axn	Manual testing	50000	6350000						3	0.489
2021-01-17T09:39:42	axn	Manual testing	80000	11280000						5	1.377
2021-01-26T01:59:50	axn	Manual testing	80000	11280000						10	2.754
2021-06-21T06:34:57	daveward2005	d12436	50000	5000000	30009676728507436540631	74.668	3	2	4509723704158779	3	0.436

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	8E196B95DA62E0__	0.343

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-06-22T08:09:56

kutens

sol

30009676728507436540631

4E4CD18B76E4A395

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 = 10000000, B2 = 400000000 (P-1 stage 2)

B1 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

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

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 415800, B2 = 4158000 (P-1 stage 2)

B1 = 415800 (P-1 stage 1)

B1 = 60000, B2 = 1050000 (P-1 stage 2)

B1 = 99360 (P-1 stage 1)

B1 = 79680 (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

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-02T19:48:45+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