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Nov 14, 2023 at 17:01 comment added GH from MO Hua proved in 1938 that every sufficiently large positive integer of the form $24k+5$ can be written as $x_1^2+\dotsb+x_5^2$ where each $x_j$ is a prime number. It follows that every sufficiently large positive integer can be written as $x_1^2+\dotsb+x_9^2$, where each $x_j$ is a prime number or $0$ or $1$.
Nov 14, 2023 at 15:15 history answered gnasher729 CC BY-SA 4.0