M12 329 657 Mersenne number exponent details

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is 2 ^12329657 - 1

has 3711597 decimal digits

takes 4.747 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	E7A260123EAFA4DA	double-checked
PRP	84B48758D6E41F0D	PRP-tested

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	4.8343	64.7059%	400000	266270550	8.3098	8.6400%	13.1440	67.7553%
Target	2⁶⁸	4.8343	64.7059%	90000	2200000	0.1144	3.0841%	4.9487	65.7944%
Difference	-	-	-	+310000	+264070550	+8.1953	+5.5559%	+8.1953	+1.9609%

Known prime factors (1 factor, 66.1 bits, 0.00053630% 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
12329657	80409400182483597697	20	66.124	3260812534464 2⁶ × 3 × 10597 × 1602661	2015-03-11	10597	1602661	2.2746	0.0543	0.0910

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-02-25	ANONYMOUS	v4_computers	140000	1750000		-	MISSED FACTOR!	-	-	0.127	-	-	3.145%
2022-01-30	nordi	sweet16_30.8b8	400000	400000		-		-	-	0.223	-	-	2.149%
2022-02-27	nordi	sweet16_30.8b10	400000	266270550		-	skipped known factor: 80409400182483597697	-	-	8.310	-	-	8.640%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-15	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.289	-	-
2013-07-27	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.303	-	-
2013-09-18	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.606	-	-
2015-03-11	Tha	Manual testing	2⁶⁶	2⁶⁷	80409400182483597697	66.124	20	1.077	12.03	2.729
2022-04-10	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	2.424	-	-

ECM factoring results:
No ECM results for M12329657

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-07-03	ANONYMOUS	v4_computers	E7A260123EAFA4DA	4.747
2001-09-22	ANONYMOUS	v4_computers	E7A260123EAFA4DA	4.747

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-03-07

XZT

3050Micro1

80409400182483597697

84B48758D6E41F0D

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 = 400000, B2 = 266270550 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 140000, B2 = 1750000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 68

TF double-checked to: 67.7

2⁵⁰

2⁶⁰

2⁷⁰

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