1600.41 – Primes Conjecture

True or false: Whenever $N$ , $N - 10$ , $N + 30$ , and $N + 60$ are all prime numbers, then so is $N + 90$ .

Solution

False: When you come to $N = 617$ , you'll get 607, 647, and 677, all primes, but $707 = 101 \times 7$ is not.