[ASSIGNMENT] : make the most efficient prime testing code

Question

In sololearn challenges we have seen several prime testing methods: "naive" ( test if p is even, and all the odd divisors until sqrt(p)), "fast" (using Miller Rabin, see example hereafter), sieve (google it or see example hereafter)...

Your challenge is to make the fastest prime testing software which leverage the correct method depending on the size of the numbers in the two following cases
prime(p) [returns true is p is prime]
primes(a,b) [returns the list of primes between a and b]

Answer 1

Sieve:
https://code.sololearn.com/c58LnOJlqfXd/?ref=app

Answer 2

Fast prime is function f hereafter
https://code.sololearn.com/cM8lUVSBV0PS/?ref=app

Answer 3

Naive prime
https://code.sololearn.com/cnU20ZM7PqAy/?ref=app