In Python:

(a) A twin prime is a prime p such that p+2 is also prime. Write a function num_twin_primes(n) that computes the number of twin primes less than n . For example num_twin_primes(10) is 2 since 3,5 are the twin primes less than 10 . You can use builtin functions such as next_prime and is_prime.

(b) Compute num_twin_primes(10^2), num_twin_primes(10^4), num_twin_primes(10^8).

(c) Based on your experiments, make a guess about the behavior of the ratio num_twin_primes(n)/n as n .