M2433953 Mersenne number exponent details

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M2433953

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>>>

is 2 ^2433953 - 1

has 732693 decimal digits

takes 0.164 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	D4099BC56A725513	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	2⁶⁷	12.2081	67.1642%	1986400	69524000	0.5550	7.8042%	12.7631	69.7268%	2.5626%
PrimeNet	2⁵⁹	0.0316	62.7119%	10000	180000	0.0019	2.5251%	0.0334	63.6534%	0.9416%
GPU72	2⁶³	0.6557	65.0794%	10000	150000	0.0017	1.3058%	0.6575	65.5354%	0.4560%
Difference	+4	+11.5524	+2.0848%	+1976400	+69374000	+0.5533	+6.4984%	+12.1057	+4.1914%	+4.1914%

Known prime factors (1 factor, 66.3 bits, 0.00272325% 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
2433953	89755256548744686743	20	66.283	18438165516907 31397 × 587258831	2015-07-05	31397	587258831	6.5555	3.1370	5.8537

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.289%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.901%
2010-11-17T11:34:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.312%
2011-01-09T14:31:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.795%
2011-01-24T12:42:00	Oscar Östlin		95000	1923750		-		-	-	0.019	-	-	2.664%
2014-05-02T10:00:00	mikr	MSI	1986400	69524000		-		-	-	0.555	-	-	7.804%
2018-09-28T17:00:35	alpertron	Manual testing	2000000	60000000	12	-		-	-	0.505	-	-	7.626%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.016	-	-
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2022-03-10T05:52:51	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.063	-	-
2009-01-10T20:55:00	Sturle Sunde	danzi.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-05T17:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.126	-	-
2013-12-04T21:13:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.403	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.807	-	-
2015-02-27T20:40:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.535	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.160 GHz-days
Estimated T-Level:	0.650

Digits	B1	Curves	Complete	FacMiss
20	11000	13 / 100	0.130	87.752%
25	50000	13 / 280	0.046	95.455%

New Calculation Method

Total ECM effort:	1.160 GHz-days
Estimated T-Level:	0.650

Digits	B1	Complete	FacMiss
20	11000	0.419	65.747%
25	50000	0.038	96.281%
30	250000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.070
50000	5000000	89755256548744686743	1	0.089

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-07T20:48:00	Chang Chia-Tche	euler06	50000	5000000						3	0.268
2010-03-04T13:23:00	unconnected	X3220--xp	50000	5000000						3	0.268
2012-03-30T23:21:00	S36049	Wolle5	50000	5000000						3	0.268
2013-12-19T14:00:00	Andy Incline	Office-PC	50000	5000000						3	0.268
2015-07-05T02:29:00	guru	w6	50000	5000000	89755256548744686743	66.283	1	2		1	0.089

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-02-08T00:00:00	ANONYMOUS	v4_computers	D4099BC56A725513	0.164
1999-03-26T00:00:00	ANONYMOUS	v4_computers	D4099BC56A725513	0.164

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:24:47

alpertron

Manual testing

89755256548744686743

F908703173686E__

2017-11-04T02:15:44

Oliver Kruse

GTX-3

89755256548744686743

F908703173686E__

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 = 1986400, B2 = 69524000 (P-1 stage 2)

B1 = 2000000, B2 = 60000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1986400 (P-1 stage 1)

B1 = 95000, B2 = 1923750 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-10T05:52:51+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