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@botahamec That is common misconception, but no, the public exponent just needs to have no common factors with p-1 and q-1.

65537 is typically used because it only has two 1 bits set which allows for faster exponentiation, and it being prime means the odds of it being a factor of p-1 or q-1 are low.

This assumes the key uses two primes as the factors of the modulus. That brings me to another common misconception, that the RSA modulus needs to be semiprime - having exactly two factors.

The math all works just fine with three or more primes.