- --- In firstname.lastname@example.org, "David Broadhurst" <d.broadhurst@...> wrote:
>Thank you David, how you find things like that is beyond me. It was a nice feeling while it lasted. :) As it stands, I have lost about all expectation that 2^2^2^2 + 3^3^3^3 is prime. One reason: what you just posted. Another reason: I just got through some fiddling and see that even small prime factors intrude into the mix at higher powerings (if I have calculated correctly).
> --- In email@example.com,
> "Mark Underwood" <mark.underwood@> wrote:
> > 1^1^1^1^1 + 2^2^2^2^2
> > If the above has been proven composite (don't know)
> > then it will greatly lower my expectation that
> > 2^2^2^2 + 3^3^3^3 is prime
> Not only is the former number composite, but
> we also know two of its prime factors:
> found by Selfridge in 1953
> found by Crandall and Dilcher in 1996
For instance if 2^2^2^2 + 3^3^3^3 is considered the fourth powering, then at the 26th powering the factor of 283 is introduced.
This same factor of 283 then reappears every 21st power after that: at the 47,68,89,110,131,etc. powering. (I think.)