M101 736 851 Mersenne number exponent details

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M101736851

<<<

is 2 ^101736851 - 1

has 30625844 decimal digits

takes 405.075 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	2⁷⁶	150.4272	64.4737 %	650000	650000	3.7527	1.4299 %	154.1799	64.9817 %
Target	2⁷⁶	150.4272	64.4737 %	650000	110000000	38.1483	3.8485 %	188.5755	65.8409 %
Difference	-	-	-	-	-109350000	-34.3956	-2.4186 %	-34.3956	-0.8592 %

Known prime factors (1 factor, 76.1 bits, 0.00007484% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
101736851	83187494794024727844737	23	76.139	408836591541568 2⁶ × 337 × 42491 × 446111	2020-12-23	42491	446111	292.00	0.3723	0.4993

P-1 results:

date	user	comp	B1	B2	BS	stage	factor	digits	bits*	GHz-days	Fac Prob
2020-12-23	storm5510	Manual testing	650000	650000		1	83187494794024727844737	23	76.139	3.775	1.430%

Trial Factoring results:

			Bits		Factor
date	userid	compid	from	to	factor	bits*	digits	GHz-days
2010-03-07	1997rj7	compw	2⁶³	2⁶⁴				0.019
2010-08-14	Torchwood Institute	HTPC-V64	2⁶⁴	2⁶⁵				0.037
2012-04-17	Corbyguy	home	2⁶⁵	2⁶⁶				0.073
2013-08-19	america64	Manual testing	2⁶⁶	2⁶⁷				0.147
2013-08-24	Preben S	Manual testing	2⁶⁷	2⁶⁸				0.294
2013-09-30	Roberto Arcieri	xxx	2⁶⁸	2⁶⁹				0.588
2013-10-29	Roberto Arcieri	xxx	2⁶⁹	2⁷⁰				1.175
2013-12-09	Lukin Dmitry	Manual testing	2⁷⁰	2⁷¹				2.350
2014-12-23	Smok_bmv	Manual testing	2⁷¹	2⁷²				4.701
2020-02-22	Niels_Mache_Nextcloud	Manual testing	2⁷²	2⁷⁴				28.21
2020-10-10	TheJudger	Manual testing	2⁷⁴	2⁷⁶				112.8

ECM factoring results:
No ECM results for M101736851

Lucas-Lehmer results:
No L-L results for M101736851

PRP results:
No PRP results for M101736851

CERT results:
No CERT results for M101736851

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 = 650000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

TF factor-bounds graph:

2⁷⁶

2⁷⁴

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

this exponent TF target: 76

TF double-checked to: 67

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

JSON version of this page

Last modified: 2024-04-17T15:19:26+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