Cryptography, Algorithms, Public Key Cryptography.
Because there are numbers z to which 2 can be mod-exponentiated to produce all the number s relatively prime to 5 (like 2⁰ = 1, 1 mod 5 = 1; 2¹ = 2, 2 mod 5 = 2 and so on) but in case of 4 there isn’t enough such exponents to produce all the relatively primes of 5 (4⁰ = 1, 1mod5 = 1; 4¹ = 4, 4mod5