Sundaram's SieveIssue 50
Step 2 — Solution
Since N lies in the array, it is equal to (2n+1)m+n for some n and m. Use this to work out 2N+1 in terms of m and n:
Since 2m+1 and 2n+1 are both integers greater than 1, this shows that 2N+1 has factors that are both greater than one, so it cannot be prime. This shows that if N lies in the array, then 2N+1 cannot be prime.