M3288953 Mersenne number exponent details

≡

M3288953

<<<

>>>

is 2 ^3288953 - 1

has 990074 decimal digits

takes 0.345 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	BE8863F3F64E88C9	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	18.1228	67.6471%	5000000	100000000	1.5497	8.3702%	19.6724	70.3551%	2.7080%
PrimeNet	2⁶⁰	0.0467	63.3333%	14000	260000	0.0042	2.7768%	0.0509	64.3515%	1.0181%
GPU72	2⁶⁴	1.0822	65.6250%	17000	280000	0.0048	1.6882%	1.0870	66.2053%	0.5803%
Difference	+4	+17.0405	+2.0221%	+4983000	+99720000	+1.5449	+6.6820%	+18.5855	+4.1498%	+4.1498%

Known prime factors (1 factor, 84.2 bits, 0.00255964% 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
3288953	21994351922396619675006481	26	84.185	3343670755160779080 2³ × 3² × 5 × 41² × 47 × 117558878579	2021-03-31	1681	117558878579	1,577,980	975.41	1,821.8

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-09T19:18:00	Carsten Kossendey	durandal	15000	191250		-		-	-	0.004	-	-	0.787%
2011-09-25T16:29:00	harlee	P4_2600	60000	1065000		-		-	-	0.017	-	-	1.939%
2014-06-26T21:22:00	ANONYMOUS	Manual testing	79515	79515		-		-	-	0.012	-	-	0.754%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	99030	99030		-		-	-	0.015	-	-	0.861%
2016-01-28T01:44:16	Jocelyn Larouche	Manual testing	383400	3834000	6	-		-	-	0.087	-	-	3.600%
2021-04-01T03:35:16	riccardo uberti	Colab_noGPU14	5000000	100000000	12	-		-	-	1.550	-	-	8.370%
2022-03-24T08:47:00	Jocelyn Larouche	Manual testing	1000000	134316000		-		-	-	1.258	-	-	7.652%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-08-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.047	-	-
2009-04-02T04:52:00	S485122	USB-Z	2⁶⁰	2⁶¹		-	-	0.047	-	-
2011-10-04T02:42:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.093	-	-
2012-12-30T00:06:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.298	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.597	-	-
2015-02-07T18:05:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.136	-	-
2015-06-29T20:47:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.272	-	-
2017-04-07T14:00:46	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.544	-	-
2018-11-19T15:52:50	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.088	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.986 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	4.986 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.072	34.231%
25	50000	0.097	90.775%
30	250000	0.006	99.404%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	2.185
50000	5000000	21994351922396619675006481	3	0.437
50000	6750000		7	1.180
50000	6800000		7	1.184

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-26T23:08:00	the_computer_geek	main_computer	50000	5000000						3	0.437
2011-10-05T15:43:00	S00030	op9020-usff	50000	5000000						3	0.437
2014-07-25T19:47:00	Pool Party	St.P.p	50000	5000000						3	0.437
2016-09-15T17:05:03	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-02-15T00:09:51	Idgo	Pentium_Desktop	50000	5000000						3	0.437
2021-01-24T21:26:29	lycorn	colab_D_1	50000	6800000						7	1.184
2021-02-23T23:04:17	lycorn	colab_ES	50000	6750000						7	1.180
2021-03-31T10:01:47	mnd9	75211frontb	50000	5000000	21994351922396619675006481	84.185	3	2	4307858769014126	3	0.437

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-26T00:00:00	ANONYMOUS	v4_computers	451C4A8473D505__	0.345

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-01T20:43:16

Joe S.

6700k

21994351922396619675006481

BE8863F3F64E88C9

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 = 5000000, B2 = 100000000 (P-1 stage 2)

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

B1 = 5000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

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

B1 = 383400 (P-1 stage 1)

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

B1 = 99030 (P-1 stage 1)

B1 = 79515 (P-1 stage 1)

B1 = 60000 (P-1 stage 1)

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

B1 = 15000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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: 2022-03-24T08:47:00+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