+249 For a certain positive integer n, n^2 gives a remainder of 4 when divided by 5, and n^3 gives a remainder of 2 when divided by 5. What remainder does n give when divided by 5?
For a positive integer n, if both n and n+2 are prime, then they are known as twin primes. For example, 59 and 61 are twin primes. Whether or not there are an infinite number of twin primes is a famous unsolved problem in number theory.
Find all positive integers n such that n, n+2, n+4 are all prime.
