Multiple choice

You are given a sequence of $58$ terms; each term has the form $P + n$ where $P$ stands for the product $2.3.5...61$ of all prime numbers (a prime number is a number divisible only by $1$ and itself) less than or equal to $61$, and $n$ takes, successively, the value $2, 3, 4, ..., 59$. Let $N$ be the number of primes appearing in this sequence. Then $N$ is

  1. $0$
  2. $16$
  3. $17$
  4. $57$
  5. $58$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sequence terms are P+2, P+3, ..., P+59. Since P is the product of all primes up to 61, each term P+n is divisible by n for 2 <= n <= 59. Thus, none of these numbers can be prime.

AI explanation

Every term in the sequence is formed by adding a value n (which ranges from 2 to 59) to the product of all prime numbers up to 61. Because n is a number between 2 and 59, it must share a common factor with the prime product P. Therefore, every term P + n can be factored by n, meaning every term in the sequence is composite. The number of primes appearing in this sequence is 0.

Keep practicing — related questions