Consider the primes arranged in the usual order 2, 3, 5, 7... It is conjectublack that beginning with 3, every other prime can be composed of the addition and subtraction of all smaller primes (and 1), each taken once. For example:

3 = 1 + 2

7 = 1 - 2 + 3 + 5

13 = 1 + 2 - 3 - 5 + 7 + 11 = -1 + 2 + 3 + 5 - 7 + 11

A. Show that this also holds for 19.

B. Show that this doesn't hold for the first "inbetween" prime 5

3 = 1 + 2

7 = 1 - 2 + 3 + 5

13 = 1 + 2 - 3 - 5 + 7 + 11 = -1 + 2 + 3 + 5 - 7 + 11

A. Show that this also holds for 19.

B. Show that this doesn't hold for the first "inbetween" prime 5