M3288889 Mersenne number exponent details

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M3288889

<<<

>>>

is 2 ^3288889 - 1

has 990055 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	E591D3A409C77FE0	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	18.1231	67.6471%	4000000	150000000	1.8206	8.7836%	19.9437	70.4888%	2.8418%
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	1.6881%	1.0870	66.2053%	0.5803%
Difference	+4	+17.0409	+2.0221%	+3983000	+149720000	+1.8158	+7.0955%	+18.8567	+4.2835%	+4.2835%

Known prime factors (1 factor, 101.4 bits, 0.00308261% 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
3288889	3307254739185510699900295338377	31	101.383	502792088633199645822692 2² × 29 × 461 × 48821 × 2282989 × 84356593	2021-04-18	2282989	84356593	5.463e+10	1.0287	1.3073

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%
2011-09-24T01:53:00	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%
2021-04-18T18:06:37	mikr	MSI	4000000	150000000	12		3307254739185510699900295338377	31	101.383	1.821	0.691	3.641	8.784%
2022-03-19T20:23:39	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	-	-
2011-09-25T16:42:00	markr	oldgamer	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:	5.066 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:	5.066 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.054	34.850%
25	50000	0.094	91.007%
30	250000	0.006	99.425%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	3050000		7	0.842
50000	5000000		29	4.225

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-28T08:04:00	paulie	iMac3.4	50000	5000000						3	0.437
2011-10-06T09:31:00	Smurgs	Praca	50000	5000000						3	0.437
2014-07-23T12:28:00	Pool Party	St.P.p	50000	5000000						3	0.437
2016-09-15T16:00:50	Dennis Schreiber	z400	50000	5000000						3	0.437
2019-02-14T17:02:25	Idgo	Pentium_Desktop	50000	5000000						3	0.437
2021-01-24T06:04:35	daveward2005	Dave2	50000	5000000						7	1.020
2021-02-22T00:48:39	Zenzoma	AM3700X_1	50000	5000000						7	1.020
2021-03-31T13:10:58	-Anonymous-	PC1	50000	3050000						7	0.842

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-07-27T00:00:00	ANONYMOUS	v4_computers	39348E32A08ABD__	0.345

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-19T11:49:10

mikr

Nitron

3307254739185510699900295338377

E591D3A409C77FE0

2021-04-25T08:02:42

Chang Chia-Tche

exbpc13

3307254739185510699900295338377

E591D3A409C77FE0

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 = 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)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-03-19T20:23:39+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