M110 278 661 Mersenne number exponent details

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is 2 ^110278661 - 1

has 33197185 decimal digits

takes 484.001 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	2⁶⁷	0.2694	59.7015%	-	-	-	-	0.2694	59.7015%
Target	2⁷⁶	138.7757	64.4737%	700000	26000000	13.2268	4.0491%	152.0025	65.9122%
Difference	-9	-138.5062	-4.7722%	-700000	-26000000	-13.2268	-4.0491%	-151.7330	-6.2107%

Known prime factors (1 factor, 37.8 bits, 0.00003426% 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
110278661	236216891863	12	37.781	1071 3² × 7 × 17	2007-09-21	9	17	2.045e-10	6.005e-5	0.0001

P-1 results:
No P-1 results for M110278661

Trial Factoring results:
No TF results for M110278661

ECM factoring results:
No ECM results for M110278661

Lucas-Lehmer results:
No L-L results for M110278661

PRP results:
No PRP results for M110278661

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

TF factor-bounds graph:

this exponent TF target: 76

TF double-checked to: 67.8

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

Last modified: 2023-04-26T21:34:10+00:00