In how many ways can 10001 be written as the sum of two primes?

a. 0

b. 1

c. 2

d. 3

e. 4

A. 0

If the sum of two numbers is odd, one number must be even and the other number must be off, because all primes except 2 are off, 2 must be one of the summands, because 10,001 = 2+9999, and 9 x 1111 is not prime, so there are no solutions.