How many prime numbers p are there such that 29 raised to the power p plus 1 is a multiple of p?

To solve this problem, we can use Fermat's Little Theorem, which states that if p is a Prime number and a is any integer, then a^p ≡ a (mod p). Given that 29^p + 1 is a multiple of p, we can rewrite this as 29^p ≡ -1 (mod p). This implies that p must be a prime of the form 4k + 1, where k is a non-negative integer. Therefore, there are infinitely many prime numbers p that satisfy the given condition.