Suppose x is the product of all the primes less than or equal to 59. How many primes appear in the set {x + 2, x + 3, x + 4, …, x + 59}?
Select:
A) 0  B) 17  C) 18  D) 23  E) 24
Since 2 * 3* 5 *... *59 is even, x is even.   As x is even, so will be x+2, x+4, x+6...... x+58, so these numbers cannot be prime.   Now x+3 is nothing but (2*3*... 59) + 3. Rewriting this as {3 * (2 * 5*.... 59)} +3.   One can observe here that the term in the curly brace is a multiple of 3 and that term plus 3 will definitely be a multiple of 3 .   (Multiple of 3 + 3 is a multiple of 3, Multiple of 59 + 59 is a multiple of 59)   As x+3 is a multiple of 3 it cannot be a prime.   Similarly x+5 can be written as {5 * (2 * 3* 7*.... 59)} +5 which is a multiple of 5.   0NSWER:0
<result>A</result>
Suppose x is the product of all the primes less than or equal to 59. How many primes appear in the set {x + 2, x + 3, x + 4, …, x + 59}?