M12 526 721 Mersenne number exponent details

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is 2 ^12526721 - 1

has 3770919 decimal digits

takes 4.823 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	F1ED6BF72B7F18C7	double-checked
PRP	8AE30B1BBDAF4893	PRP-tested

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	4.7582	64.7059%	150000	2175000	0.1453	3.3518%	4.9035	65.8889%
Target	2⁶⁸	4.7582	64.7059%	90000	2200000	0.1144	3.0913%	4.8726	65.7969%
Difference	-	-	-	+60000	-25000	+0.0309	+0.2605%	+0.0309	+0.0919%

Known prime factors (1 factor, 66.6 bits, 0.00053154% 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
12526721	110638612792548267751	21	66.584	4416104293875 3² × 5³ × 2213 × 1773803	2015-03-22	2213	1773803	1.5082	0.0551	0.1008

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-03-17	ANONYMOUS	v4_computers	150000	2175000		-	MISSED FACTOR!	-	-	0.145	-	-	3.352%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-22	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.000	-	-
2000-03-22	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2000-04-05	MadPoo	v4_computers	2¹	2⁶⁴		-	-	0.284	-	-
2013-06-20	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.298	-	-
2014-03-28	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.597	-	-
2015-03-22	Tha	Manual testing	2⁶⁶	2⁶⁷	110638612792548267751	66.584	21	0.329	12.15	0.829
2022-04-10	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	2.386	-	-

ECM factoring results:
No ECM results for M12526721

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-04-29	ANONYMOUS	v4_computers	F1ED6BF72B7F18C7	4.823
2004-08-06	monst	v4_computers	F1ED6BF72B7F18C7	4.823

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-04-16

kutens

terra

110638612792548267751

8AE30B1BBDAF4893

no

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 = 150000, B2 = 2175000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁶

2⁵⁵

this exponent TF target: 68

TF double-checked to: 67.7

2⁵⁰

2⁶⁰

2⁷⁰

Last modified: 2023-03-25T13:08:14+00:00