M418 157 Mersenne number exponent details

≡

M418157

<<<

>>>

is 2 ⁴¹⁸¹⁵⁷ - 1

has 125878 decimal digits

takes 0.004 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	-unknown-	-unknown-
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown			3000000	100000000	0.1165	34.6557%	0.1165	34.6557%
Target	2⁴⁴	0.0000	56.8182%	7000	1100000	0.0009	13.1406%	0.0009	62.4925%
Difference	-44	0.0000	-56.8182%	+2993000	+98900000	+0.1155	+21.5151%	+0.1155	-27.8369%

Known prime factors (2 factors, 125.0 bits, 0.02989504% 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
418157	51336177310471	14	45.545	61383855 3 × 5 × 13 × 17 × 18517	-	17	18517	1.736e-5	1.441e-5	2.649e-5
418157	833295525692228887296271	24	79.463	996390740430303555 3 × 5 × 601241 × 110481569557	2020-06-08	601241	110481569557	480,066	84.622	158.03

exponent	prime factors	composite factor	digits	bits*
418157	51336177310471 833295525692228887296271	42778206858958404839946414363727553641	38	125.008

1 Composite Factors:

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16	alpertron	Manual testing	3000000	100000000	12	-	skipped known factor: 51336177310471	-	-	0.116	-	-	34.656%

Trial Factoring results:
No TF results for M418157

ECM factoring results:

Total ECM effort:	10.569 GHz-days
Estimated T-Level:	26.435

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	2.967
250000	25000000		121	6.388
250000	25000000	833295525692228887296271	23	1.214

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-11-21	TJAOI	Manual testing	50000	5000000						50	0.528
2015-03-13	TJAOI	Manual testing	50000	5000000						50	0.528
2016-01-04	TJAOI	Manual testing	50000	5000000						90	0.950
2016-05-06	TJAOI	Manual testing	50000	5000000						91	0.961
2018-01-12	TJAOI	Manual testing	250000	25000000						44	2.323
2020-06-08	TJAOI	Manual testing	250000	25000000	833295525692228887296271	79.463	23	2		23	1.214
2020-06-08	TJAOI	Manual testing	250000	25000000						77	4.065

Lucas-Lehmer results:
No L-L results for M418157

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23

Oliver Kruse

Ollaptop

51336177310471

7140B4275C839C__

2017-11-02

kkmrkkblmbrbk

c4.xlarge

51336177310471

7140B4275C839C__

2020-04-18

Oliver Kruse

AddPrpType5

51336177310471

238BFD76F87031__

2020-06-08

CrypticClue

cruncher

51336177310471

833295525692228887296271

238BFD76F870311B

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

this exponent TF target: 44

TF double-checked to: 67.9

ECM T-Level=26.44 ~= 71-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

JSON version of this page

Last modified: 2023-10-02T12:12:48+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront