M5 227 Mersenne number exponent details

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is 2 ⁵²²⁷ - 1

has 1574 decimal digits

takes 0.000 GHz-days to do one PRP test

Has been fully factored.

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
PRP	-unknown-	-unknown-
Cofactor is a certified prime

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	5,684.6982	80.5970%	-	-	-	-	5,684.6982	80.5970%
Target	2⁴⁴	0.0004	70.4545%	500	50000	0.0000	1.0331%	0.0004	70.7598%
Difference	+23	+5,684.6978	+10.1425%	-500	-50000	0.0000	-1.0331%	+5,684.6978	+9.8372%

Known prime factors (4 factors, 5,227.0 bits, 100.00000000% known):

Remaining cofactor is a certified-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5227	1129033	7	20.107	108 2² × 3³	-	27	27	2.735e-11	2.481e-9	5.048e-9
5227	47126633	8	25.490	4508 2² × 7² × 23	2009-03-05	49	49	1.690e-9	4.502e-9	9.162e-9
5227	227482218017	12	37.727	21760304 2⁴ × 839 × 1621	2009-03-05	839	1621	3.582e-6	8.100e-8	1.569e-7
5227	hide decimal representation P1549 click to show decimal representation	1,549	5,143.676		2009-03-05

4 Composite Factors:

P-1 results:
No P-1 results for M5227

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2009-03-05	ANONYMOUS	Manual testing	?	?	227482218017	37.727	12	7.88519e-8	0.000	0.000
2009-03-05	ANONYMOUS	Manual testing	?	?	47126633	25.490	8	8.34455e-10	0.000	1.13159e-6

ECM factoring results:
No ECM results for M5227

Lucas-Lehmer results:
No L-L results for M5227

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-09

kkmrkkblmbrbk

c4.large

1129033

47126633

227482218017

PRP

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

TF factor-bounds graph:

2

this exponent TF target: 44

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

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