Problem: You are given a sequence of terms, each of which is of the form , where the first term is the product of all prime numbers (a prime number is one divisible only by and itself) beginning with and ending with , and the second term is one of the natural numbers, taken in order, beginning with and ending with , inclusive. Let N be the number of primes appearing in this sequence. Then is:
Answer Choices:
A.
B.
C.
D.
E.
Solution:
When is prime each member of the sequence is divisible by . When is composite each member of the sequence is divisible by all the prime numbers that divide . It follows that each member of the sequence is composite, so that ( ) is the correc choice.