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

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

Consecutive prime numbers are going to be close to one another in the number line, and therefore not very different from the square of the number midway between them.  We can thus try to locate the prime numbers in question by looking between the square root of 1000 (31.6) and 1500 (38.7).

 

In this immediate vicinity, the only prime numbers are 31 and 37, which are consecutive - no other prime numbers lie between them.  The product of 31 and 37 is 1147, which is between 1000 and 1500.  This meets the description above, so Martiza's PIN must be 1147.