Question

primes of form p^2 + 2^p

Answer 1

p is prime

Answer 2

What exactly is this?

Answer 3

are you asking is there or not primes of the form ?

Answer 4

Yes, im trying to find all prime of form p^2 + 2^p
where p is a prime

Answer 5

the only that gives primes is 3
let p^2 be an odd prime >3

p^2+2^p mod 3
(1)^2+(-1)^p mod 3= 0 mod 3
(2)^2+(-1)^p mod 3 =0 mod 3

Answer 6

nice question ...

Answer 7

i made a typo... let p be odd prime>3 and not p^2 =)

Answer 8

Awesome!

Answer 9

\(3\mid (p^2+2^p)\) for all \(p\gt 3\)

Answer 10

=]

Answer 11

hmm