16

This number is a composite.

2²² is the smallest number n such that 3 + n, (3*5) + n, (3*5*17) + n, (3*5*17*257) + n, (3*5*17*257*65537) + n are all primes. Note that 3, 5, 17, 257 and 65537 are the known Fermat primes, with the property (F₀*F₁*F₂*...*F_n-1) + 2 = F_n [Capelle]