1960 AHSME Problem 33

You are given a sequence of 58 terms; each term has the form P+n where P stands for the product 2 \times 3 \times 5 \times\ldots \times 61 of all prime numbers less than or equal to 61, and n takes, successively, the values 2, 3, 4,\ldots, 59. Let N be the number of primes appearing in this sequence. Then N is:

\textbf{(A)}\ 0\qquad \textbf{(B)}\ 16\qquad \textbf{(C)}\ 17\qquad \textbf{(D)}\ 57\qquad \textbf{(E)}\ 58

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.