M3128033 Mersenne number exponent details

≡

M3128033

<<<

>>>

is 2 ^3128033 - 1

has 941632 decimal digits

takes 0.266 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	1E31E14B85BD2096	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	19.0551	67.6471%	3128033	637437570	4.6510	10.4096%	23.7061	71.0149%	3.3678%
PrimeNet	2⁶⁰	0.0491	63.3333%	13000	240000	0.0031	2.6465%	0.0522	64.3037%	0.9704%
GPU72	2⁶⁴	1.1379	65.6250%	15000	240000	0.0034	1.5421%	1.1412	66.1551%	0.5301%
Difference	+4	+17.9172	+2.0221%	+3113033	+637197570	+4.6476	+8.8675%	+22.5648	+4.8598%	+4.8598%

Known prime factors (1 factor, 86.1 bits, 0.00275216% 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
3128033	82271775024070517322625399	26	86.089	13150720440620434203 3 × 7 × 64013 × 2701871 × 3620741	2018-12-13	2701871	3620741	9,177,424	0.3396	0.6786

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.251%
2009-07-03T00:50:00	Carsten Kossendey	leela	15000	180000		-		-	-	0.003	-	-	0.764%
2011-08-31T06:19:00	Squeeky_Squirrel	T7500_2200	105000	2152500		-		-	-	0.027	-	-	2.573%
2011-09-22T00:00:00	ANONYMOUS	v4_computers	10000	10000		-		-	-	0.001	-	-	0.148%
2016-10-01T12:25:16	Squeeky_Squirrel	i5-5250U_1600	195000	5460000	12	-		-	-	0.059	-	-	3.526%
2018-07-17T23:14:17	Jocelyn Larouche	low 4M	692144	2076432		-		-	-	0.095	-	-	3.211%
2018-07-18T06:34:20	Jocelyn Larouche	low 4M	692144	2768576		-		-	-	0.099	-	-	3.479%
2018-07-18T23:15:57	Jocelyn Larouche	low 4M	692144	4152864		-		-	-	0.109	-	-	3.861%
2018-12-13T17:28:47	mikr	MSI	3000000	100000000	12		82271775024070517322625399	26	86.089	1.022	0.532	2.045	8.055%
2021-11-20T20:53:51	Jocelyn Larouche	Manual testing	3128033	3128033		-		-	-	0.386	-	-	3.766%
2021-12-19T09:29:28	Jocelyn Larouche	Manual testing	3128033	108997350		-	skipped known factor: 82271775024070517322625399	-	-	1.098	-	-	8.188%
2021-12-22T09:19:32	Jocelyn Larouche	Manual testing	3128033	637437570		-	skipped known factor: 82271775024070517322625399	-	-	4.651	-	-	10.410%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-06T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.049	-	-
2009-04-13T05:58:00	S485122	USB-A	2⁶⁰	2⁶¹		-	-	0.049	-	-
2011-11-14T01:33:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.098	-	-
2013-01-03T08:41:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.314	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.628	-	-
2015-02-11T09:10:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.194	-	-
2015-06-14T13:51:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.389	-	-
2021-01-03T02:39:41	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.389	-	-
2017-04-16T02:34:53	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.778	-	-
2021-02-25T15:38:25	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.56	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.106 GHz-days
Estimated T-Level:	0.900

Digits	B1	Curves	Complete	FacMiss
20	11000	18 / 100	0.180	83.451%
25	50000	18 / 280	0.064	93.763%

New Calculation Method

Total ECM effort:	2.106 GHz-days
Estimated T-Level:	0.900

Digits	B1	Complete	FacMiss
20	11000	0.581	55.954%
25	50000	0.052	94.888%
30	250000	0.003	99.677%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		18	2.106

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-06-19T21:07:00	James Hintz	4115	50000	5000000						3	0.351
2011-07-28T00:03:00	Smurgs	Praca	50000	5000000						3	0.351
2014-01-01T11:35:00	timc995	ec2_win	50000	5000000						3	0.351
2016-06-04T13:23:05	remvad	home	50000	5000000						3	0.351
2017-12-29T20:42:18	Conductor	My	50000	5000000						3	0.351
2019-01-26T13:55:08	Conductor	Manual testing	50000	5000000						3	0.351

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-12-23T00:00:00	ANONYMOUS	v4_computers	1E31E14B85BD2096	0.266

PRP results:

date

userid

compid

cofactors

res64

PRP

2018-12-15T03:58:41

oodaira

com1

82271775024070517322625399

910EFE28109247AB

2018-12-15T21:26:08

kkmrkkblmbrbk

c5.large

82271775024070517322625399

910EFE28109247AB

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 = 3128033, B2 = 637437570 (P-1 stage 2)

B1 = 3128033, B2 = 108997350 (P-1 stage 2)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3128033 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 692144, B2 = 4152864 (P-1 stage 2)

B1 = 692144, B2 = 2768576 (P-1 stage 2)

B1 = 692144, B2 = 2076432 (P-1 stage 2)

B1 = 692144 (P-1 stage 1)

B1 = 195000, B2 = 5460000 (P-1 stage 2)

B1 = 105000, B2 = 2152500 (P-1 stage 2)

B1 = 195000 (P-1 stage 1)

B1 = 105000 (P-1 stage 1)

B1 = 15000, B2 = 180000 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

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

Last modified: 2021-12-22T09:19:32+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