| Conjecture: there are no other terms.
The finiteness of this sequence would follow from Cramer's conjecture that lim sup (p(n+1)-p(n))/log(p(n))^2 = 1. - Dean Hickerson, Dec 12 2006
The finiteness of this sequence would imply that, for every sufficiently large positive integer n, there is a prime between n^2 and (n+1)^2. Except for the "sufficiently large", that's Legendre's conjecture, which is still unproved. - Dean Hickerson, Dec 12 2006
There are no other terms less than 218034721194214273 (assuming that the extended table of terms in A002386 is correct). - Dean Hickerson, Dec 12 2006
The evidence suggests that for any k, the number of primes with p < gap(p)^k is finite (this sequence being the special case k = 2), where gap(p) is the difference between p and the next prime. - David W. Wilson, Dec 13, 2006
Primes for which sqrt(A000040(n)) < A001223(n).
| 