What prime numbers less than 100 are the sum of two square numbers?

Answer 1

The prime numbers less than 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97. The square numbers that are applicable are 1, 4, 9, 16, 25, 49, 64 and 81.

Of these primes, those that can be written as sums of two squares are as follows (with the square numbers in brackets):

• 2 (1 + 1);
• 5 (4 + 1);
• 13 (4 + 9);
• 17 (1 + 16);
• 29 (4 + 25);
• 41 (16 + 25);
• 53 (4 + 49);
• 73 (9 + 64);
• 89 (25 + 64);
• 97 (16 + 81).