Question

Hi. What is the smallest number that can be written in 6 ways as the sum of the squares of 3 primes? Also, please list them as well.

Answer 1

2019 is the smallest number.

Here are the ways:

$7^2+11^2+43^2$

$7^2+17^2+41^2$

$13^2+13^2+41^2$

$11^2+23^2+37^2$

$17^2+19^2+37^2$

$23^2+23^2+31^2$