M21 055 453 Mersenne number exponent details

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is 2 ^21055453 - 1

has 6338323 decimal digits

takes 14.922 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	1.4112	62.6866%	-	-	-	-	1.4112	62.6866%
Target	2⁶⁹	5.6701	63.7681%	150000	22500000	1.4054	3.7852%	7.0755	65.1396%
Difference	-2	-4.2589	-1.0815%	-150000	-22500000	-1.4054	-3.7852%	-5.6643	-2.4530%

Known prime factors (2 factors, 109.8 bits, 0.00052157% 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
21055453	9068162498041	13	43.044	215340 2² × 3 × 5 × 37 × 97	-	37	97	8.962e-8	4.138e-5	7.738e-5
21055453	126353674861051882031	21	66.776	3000497658755 5 × 71 × 349 × 24218069	2020-09-09	349	24218069	1.1954	1.3562	2.5324

1 Composite Factors:

P-1 results:
No P-1 results for M21055453

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2020-09-09	TJAOI	Manual testing	2⁶⁶	2⁶⁷*	126353674861051882031	66.776	21	0.494	34.50	1.142

ECM factoring results:
No ECM results for M21055453

Lucas-Lehmer results:
No L-L results for M21055453

PRP results:
No PRP results for M21055453

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

10²

10³

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁶⁷

this exponent TF target: 69

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

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