Ravi claims that 2n−12^n - 12n−1 is prime for every integer n⩾2n \geqslant 2n⩾2. Disprove Ravi's claim.
Sian claims that if n2 n^2\,n2 is a multiple of 4 then n n\,n must be a multiple of 4. Disprove Sian's claim.