detailed solution

1. Apply the Sieve Process from 200 to 300. 2. Let p be an odd prime not equal to 5. Prove that either p- - 1 or p + 1 is divisible by 10. 3. Prove that vp is irrational for any prime p. 4. Let p,, be the oth prime. Show by Mathematical Induction that Vn > 5, p,, > 2n - 1. 5. Numerical evidence makes it plausible that there are infinitely many primes p such that p + 50 is also prime. List 10 of these primes