If 1 is not counted as the square of a prime, then nonnegative numbers 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 19, 23 are not a sum of squares of primes (specifically, not a sum of terms equal to 4 or 9). It looks as if at most 8 squares of primes are sufficient to add to any other nonnegative number, and are necessary for certain arbitrarily large numbers.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of David Wilson Sent: Wednesday, September 07, 2016 8:30 PM To: 'math-fun' Subject: [math-fun] Eight prime square theorem?
Lagrange's four square theorem states that every nonnegative integer is a sum of four squares. Empirically, it looks as if every nonnegative integer is a sum of 8 squares of primes (counting 1 as prime). It looks as if arbitrarily large numbers require 8 terms.
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