Problems & Puzzles: Puzzles Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k Lets define the "average prime number" APN(k) as S(Pk)/k, where S(Pk) is the sum of the first k prime numbers. It happens that this number very few times is an integer. I have calculated the first five times it does:
Can you get the following 3 cases ? (see Puzzle 18 for similar questions about sum of consecutive primes) Jo Yeong Uk (1/12/98) has found the following first three solutions to APN(k). Jack Brennen (21/05/99) found the fourth solution.
*** Giovanni Resta wrote (Nov. 2004):
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