> If Pn is the nth pentagonal number then
> Pn = (3*n 1)*n/2 = 1 + 4 + 7 +
+ (3*n - 2)
> Can anyone find 2 primes p and q so that q = 3*n 2 and p = Pn ?
There is no such pair. The only prime pentagonal number is P2 == 5;
in that case, q is 4 and is thus not prime.
It shouldn't be too hard to figure out why 5 is the only prime
> Hexagonal sums are of the form Hn where
> Hn = 1 + 6 + 6 +
+ 6 = 6*n 5 so as 6 is not prime we won't
> find a p, q pair for hexagonal sums. However as all odd primes > 3
> are of the form 6*n 1 or 6*n 5 then about half of the primes are
> also hexagonal numbers!
Not correct. Hexagonal numbers are numbers of the form:
(4*n-2)*n/2, or (2*n-1)*n.
There are no prime hexagonal numbers.