M3 019 200 113 Mersenne number exponent details

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is 2 ^3019200113 - 1

has 908869797 decimal digits

takes 580,986.355 GHz-days to do one PRP test

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	2⁷¹	0.1583	54.9296%	-	-	-	-	0.1583	54.9296%
Target	2⁹¹	166,099.3172	64.8352%	15000000	4500000000	72,366.3969	4.1395%	238,465.7141	66.2908%
Difference	-20	-166,099.1589	-9.9056%	-15000000	-4500000000	-72,366.3969	-4.1395%	-238,465.5558	-11.3612%

Known prime factors (1 factor, 68.6 bits, 0.00000227% 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
3019200113	443465995327708173721	21	68.587	73440974220 2² × 3 × 5 × 1224016237	2020-02-17	5	1224016237	0.0282	18,608	34,754

P-1 results:
No P-1 results for M3019200113

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2020-11-05	ramgeis	r4mg31s	2¹	2⁶⁹	443465995327708173721	68.587	21	0.028	1,190,520	0.058
2020-02-17	ramgeis	r4mg31s	2⁶⁸	2⁷¹	443465995327708173721	68.587	21	0.008	1,190,520	0.058

ECM factoring results:
No ECM results for M3019200113

Lucas-Lehmer results:
No L-L results for M3019200113

PRP results:
No PRP results for M3019200113

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

10⁰

10¹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷¹

2⁶⁹

this exponent TF target: 91

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

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