- N and N+2 are both composite, and the smallest prime that divides either N or N+2 is P.
- For any positive integer M<N such that M and M+2 are both composite, either M or M+2 is divisible by some prime less than P.
- N+6 and N+8 are both composite, and the smallest prime that divides either N+6 or N+8 is greater than P.