M12067273 Mersenne number exponent details

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is 2 ^12067273 - 1

has 3632612 decimal digits

takes 4.646 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	D95CAA090988FCF3	double-checked
PRP	B3F76C8CB9830D5F	PRP-tested

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	4.9394	64.7059%	140000	1925000	0.1324	3.2072%	5.0718	65.8378%
Target	2⁶⁸	4.9394	64.7059%	80000	2000000	0.1031	2.9436%	5.0424	65.7448%
Difference	-	-	-	+60000	-75000	+0.0294	+0.2636%	+0.0294	+0.0931%

Known prime factors (1 factor, 66.2 bits, 0.00054895% 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
12067273	87345758061474584473	20	66.243	3619117511532 2² × 3³ × 19 × 23 × 43 × 1783319	2015-02-08	43	1783319	2.1278	0.0543	0.1013

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-08	ANONYMOUS	v4_computers	140000	1925000		-	MISSED FACTOR!	-	-	0.132	-	-	3.207%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-02-23	ANONYMOUS	v4_computers	2¹	2⁶⁴		-	-	0.295	-	-
2013-09-23	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.310	-	-
2013-10-03	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.619	-	-
2015-02-08	Tha	Manual testing	2⁶⁶	2⁶⁷	87345758061474584473	66.243	20	0.904	9.453	1.839
2022-04-10	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	2.477	-	-

ECM factoring results:
No ECM results for M12067273

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-02-10	ANONYMOUS	v4_computers	D95CAA090988FCF3	4.646
2004-05-25	Team Prime Rib	v4_computers	D95CAA090988FCF3	4.646
2004-07-26	ANONYMOUS	v4_computers	D95CAA090988FCF3	4.646

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-01-14

RichD0

Linux-5

87345758061474584473

B3F76C8CB9830D5F

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 = 140000, B2 = 1925000 (P-1 stage 2)

B1 = 140000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-04-10T07:00:40+00:00