Problems & Puzzles: Puzzles

Puzzle 375. Powers which are the sum of initial primes.

In May 2001 David Wilson & Vladeta Jovovic found 5 cases where the sum of the initial primes is a square (A061890):

a(n)= 100, 25633969, 212372329, 292341604, 3672424151449, [219704732167875184222756 missed, but calculated later by G. Resta in May 2003]

Jud Mc Cranie & Giovanni Resta found six cases (May 2003) that the sum of the sum of the first primes is a square (A033997, A033998):

b(n)= 9, 2474, 6694, 7785, 709838, 126789311423

c(n)= 23, 22073, 67187, 79427, 10729219, 3531577135439

All this was the matter of Puzzle 9 in these pages, a very old puzzle, indeed. There you can read an old challenge by Honaker: "no one S(k) perfect cube has been found"

Perhaps it's time to attack again these questions.

Q1. Get c(7)

Q2. Find one single example for the Honaker's question.




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