14. There is reason to believe (but it has never been proved) that there are infinitely many primes which are the sum of

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14 There Is Reason To Believe But It Has Never Been Proved That There Are Infinitely Many Primes Which Are The Sum Of 1 (78.54 KiB) Viewed 30 times

This is a number theory problem
14. There is reason to believe (but it has never been proved) that there are infinitely many primes which are the sum of the squares of three different prime numbers (the smallest example is 83 = 3² +5² + 72). Let p = pi + p² + p3, where p, P₁, P2, and p3 are primes. Use congruences (mod 3) to show that one of the three primes P₁, P2, and p3 is, in fact, 3.