24

This number is a composite.

The 24th prime number is 89. The sum of the first 24 prime numbers is 963. Note that 89 mod 24, 963 mod 24, 963 mod 89, 963 mod (89 + 24), 963 mod (89 - 24), 963 mod (89 mod 24), and the sum of the prime factors of 963 are all prime! [Ranta]