Chapter 6.5, Problem 79ES

To determine

(a)

Whether the statement'There are infinitely many twin primes' is a theorem or a conjecture.

To determine

(b)

Whether the statement'There are infinitely many primes of the form$n^2+1$' is a theorem or a conjecture.

To determine

(c)

Whether the statement'There is always a prime between n and 2n for$n\ge 2$' is a theorem or a conjecture.

To determine

(d)

Whether the statement'There is always a prime between$n^2$and${(n+1)}^2$' is a theorem or a conjecture.

To determine

(e)

Whether the statement'Every odd number greater than 5 can be written as the sum of threeprimes'is a theorem or a conjecture.

To determine

(f)

Whether the statement'Every positive even number can be written as the difference of twoprimes'is a theorem or a conjecture.