reviewed

approved

proposed

reviewed

editing

proposed

Least prime p of the form k^2+1 such that such that p == A002496(n) (mod A002496(n+1)) with p>A002496(n), or 0 if no such p exists.

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

Michel Marcus: ok; I get same terms

We state a conjecture which shows that two prime numbers of the form k^2+1 A002496(n) and A002496(n+1) are related to a third prime number p of the same form, p > A002496(n).

proposed

editing

Michel Lagneau: Right! Michel. Comments corrected.

editing

proposed

Conjecture:: Consider the smallest prime p of the form k^2+1 such that p is congruent to A002496(n) modulo q, q prime of the form m^2+1 > A002496(n). Then q = A002496(n+1).

Consider the smallest prime p of the form k^2+1 such that p is congruent to A002496(n) modulo q, q prime of the form m^2+1 > A002496(n). Then q = A002496(n+1).

Corollary:: For any pair (A002496(n), A002496(n+1)), there exist two integers m, k such that A002496(m) = A002496(n) + k*A002496(n+1), m>n+1 and n=1,2,3,...

For any pair (A002496(n), A002496(n+1)), there exist two integers m, k such that A002496(m) = A002496(n) + k*A002496(n+1), m>n+1 and n=1,2,3,...

reviewed

editing

Michel Marcus: I don't see why you need the paragraph: "We state a conjecture .... ", when the Conjecture is stated in the next paragraph ???