1.

(A) Show that every odd number that is larger or exactly 17 can be written as the sum of two composite numbers.

(B) Show that every even number that is larger or exactly 20 can be written as the sum of two composite numbers.

2. Let x be a natural number. Prove that the numbers x!+2, x!+3, x!+4, . . . , x!+x are composite numbers.