Problems & Puzzles: Conjectures Conjecture 5. Are there infinitely many primes of the form n^{2}+1? It’s believed that there are infinite primes of the form n^{2}+1. Even more than that, Hardy & Littlewood guessed that the number of such primes less than n, P(n), was asymptotic to c.sqrt(n)/ln(n). And it happens that c~ 1.3727 =P {1[(1)^{(p1)/2}]/[p1]}, where the product is taken over all the odd primes. (Ref. 2, pp. 45) Solution Daniel Gronau wrote (8/10/01):
***





