M12 497 273 Mersenne number exponent details

≡

is 2 ^12497273 - 1

has 3762055 decimal digits

takes 4.811 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	DC02D95D44B4330B	double-checked
PRP	F10FF845F91B87A7	PRP-tested

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁸	4.7694	64.7059%	400000	428459850	13.2427	9.1651%	18.0122	67.9406%
Target	2⁶⁸	4.7694	64.7059%	90000	2200000	0.1144	3.0902%	4.8838	65.7966%
Difference	-	-	-	+310000	+426259850	+13.1283	+6.0748%	+13.1283	+2.1441%

Known prime factors (1 factor, 66.7 bits, 0.00053360% 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
12497273	118699051144507394839	21	66.686	4748998087203 3 × 17 × 257 × 409 × 885881	2015-03-20	409	885881	2.2542	0.0272	0.0503

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-06-17	Kprime	v4_computers	150000	2100000		-	MISSED FACTOR!	-	-	0.143	-	-	3.323%
2022-03-28	nordi	sweet16_30.8b11	400000	400000		-		-	-	0.223	-	-	2.153%
2022-04-07	nordi	sweet16_30.8b14	400000	428459850		-	skipped known factor: 118699051144507394839	-	-	13.24	-	-	9.165%

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	2⁶⁴		-	-	0.285	-	-
2013-06-25	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.299	-	-
2014-03-03	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.598	-	-
2015-03-20	Tha	Manual testing	2⁶⁶	2⁶⁷	118699051144507394839	66.686	21	1.072	12.13	2.703
2022-04-10	LordJulius	Manual testing	2⁶⁷	2⁶⁸		-	-	2.392	-	-

ECM factoring results:
No ECM results for M12497273

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2001-08-26	Kprime	v4_computers	DC02D95D44B4330B	4.811
2004-09-02	ANONYMOUS	v4_computers	DC02D95D44B4330B	4.811

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-04-10

Poao

office-CN2

118699051144507394839

F10FF845F91B87A7

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 = 428459850 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 150000, B2 = 2100000 (P-1 stage 2)

B1 = 150000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

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