Problems & Puzzles: Conjectures Conjecture 5. Are there infinitely many primes of the form n2+1? Its believed that there are infinite primes of the form n2+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)(p-1)/2]/[p-1]}, where the product is taken over all the odd primes. (Ref. 2, pp. 4-5) Solution Daniel Gronau wrote (8/10/01):
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