M33 853 549 Mersenne number exponent details

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is 2 ^33853549 - 1

has 10190934 decimal digits

takes 40.060 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	73C6FFB9CF474F75	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷¹	14.1220	63.3803%	600000	15500000	2.4224	5.0358%	16.5444	65.2244%
Target	2⁷¹	14.1220	63.3803%	240000	56000000	5.6244	3.8381%	19.7464	64.7858%
Difference	-	-	-	+360000	-40500000	-3.2020	+1.1977%	-3.2020	+0.4386%

Known prime factors (1 factor, 81.6 bits, 0.00024105% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
33853549	3672356451270601235062969	25	81.603	54238869479690316 2² × 3³ × 59 × 967 × 12641 × 696349	2015-01-23	12641	696349	14,579	0.0856	0.1216

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-07-13	ANONYMOUS	v4_computers	395000	10171250		-	MISSED FACTOR!	-	-	1.592	-	-	4.423%
2015-01-23	riccardo uberti	Xeon12C	600000	15500000	12		3672356451270601235062969	25	81.603	2.422	80.12	4.845	5.036%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2004-07-13	ANONYMOUS	v4_computers	2¹	2⁶⁸		-	-	1.761	-	-
2013-01-03	Carsten Kossendey	Manual testing	2⁶⁸	2⁶⁹		-	-	1.766	-	-
2013-02-03	bcp19	Manual testing	2⁶⁹	2⁷⁰		-	-	3.532	-	-
2013-02-03	bcp19	Manual testing	2⁷⁰	2⁷¹		-	-	7.064	-	-

ECM factoring results:
No ECM results for M33853549

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-11-22	ANONYMOUS	v4_computers	73C6FFB9CF474F75	40.06
2005-04-26	SRS Technology	v4_computers	35474AB2396F2A3A	40.06

PRP results:
No PRP results for M33853549

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 = 600000, B2 = 15500000 (P-1 stage 2)

B1 = 395000, B2 = 10171250 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 395000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

this exponent TF target: 71

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-06-05T21:50:05+00:00