Consider the Euclid numbers defined by E_k congruent 1 + p_k #, where p_k is the kth prime and p# is the primorial. The first few values of E_k are 3, 7, 31, 211, 2311, 30031, 510511, ... (OEIS A006862). Now let q_k be the next prime (i.e., the smallest prime greater than E_k), q_k = p_(1 + π(E_k)) = p_(1 + π(1 + p_k #)), where π(n) is the prime counting function. The first few values of q_k are 5, 11, 37, 223, 2333, 30047, 510529, ... (OEIS A035345).

Andrica's conjecture | Euclid number | primorial