This number is known as C5, after Catalan. It's mentioned in Dickson's History

of Numbers.

http://mathworld.wolfram.com/Catalan-MersenneNumber.html
Noll/Caldwell have tested it against possible divisors

up to 10^51. At the moment, the only hope for deciding

Catalan's conjecture if finding a divisor.

Ed Pegg Jr

--- grostoon <

grostoon@...> wrote:

> --- In primenumbers@yahoogroups.com, "Jon Perry" <perry@g...> wrote:

> >

> > Probably not the first to spot this, but

> >

> > 2^2-1=3

> > 2^3-1=7

> > 2^7-1=127

> > 2^127-1=170141183460469231731687303715884105727

> >

> > hence 2^170141183460469231731687303715884105727-1 stands a high

> probability

> > of being prime.

> >

> > Jon Perry

> > perry@g...

> > http://www.users.globalnet.co.uk/~perry/maths/

> > http://www.users.globalnet.co.uk/~perry/DIVMenu/

> > BrainBench MVP for HTML and JavaScript

> > http://www.brainbench.com

> >

>

> Hi Jon,

>

> Compute gcd(n^17 + 9, (n+1)^17 + 9) for n = 1, 2, 3, 4, ...

> You will found that it's always 1. You can try for all n < 10^3,

> 10^4, ... 10^20, ... 10^50, it's always 1.

>

> So can we conclude with a "high probability" that the gcd is actually

> always 1 ?

>

> Then, let's try n=8424432925592889329288197322308900672459420460792433

>

> J-L

>

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