Question

Maritza remembers her PIN because it is the product of two consecutive prime numbers that is between 1000 and 1500. What is her PIN?

Answer 1

PIN number is `31` and `37`

Explanation:

If `n` is smaller of the primes,

the product of primes is of the order of `n^2`, in fact slightly greater.

Now integers with squares between `1000` and `1500` are

`{32,33,34,35,36,37,38}` of which only `37` is prime.

The prime number before `37` is `31` and after it is `41`.

As `37xx41=1517` and `31xx37=1147`

PIN number is `31` and `37`.