Twin primes are pairs of numbers pp and p+2p+2 such that both are primes—for instance, 5 and 7, 11 and 13, 41 and 43. The Twin Prime Conjecture says that there are infinitely many twin primes.
Let TwinPrime(n)TwinPrime(n) be a predicate that is true if nn and n+2n+2 are twin primes. Which of the following formulas, interpreted over positive integers, expresses that there are only finitely many twin primes?
- ∀m.∃n.m≤n∀m.∃n.m≤n and not(TwinPrime(n))
- ∃m.∀n.n≤m∃m.∀n.n≤m implies TwinPrime(n)
- ∀m.∃n.n≤m∀m.∃n.n≤m and TwinPrime(n)
- ∃m.∀n.∃m.∀n. TwinPrime(n) implies n≤m