martiza remembers her pin because it is between 1000 and 1500 and it is the product of 2 consecutive prime numbers

Question

what is martiza's pin?

Answer 1

Hi Danner,

 

Need two variables for this, one of the numbers can be x (the smaller prime) and the other y (the larger prime number).  

 

1000 < xy < 1500

 

 

If we square root everything,  we get

 

31.62 < sqrt (xy) < 38.73

 

And since prime numbers are whole numbers, one of our prime numbers must lie between 32 and 38.

 

The prime numbers between 32 and 38  is only 37.   

 

So the next prime number after 37 is 41,  if this were the larger of the primes, the next smaller is 31.

 

So Martiza's PIN is either 37 *41 = 1517 which is out of the given range b/c it is bigger than 1500.

 

Or it is 31 * 37 =1147 which falls between 1000 and 1500.

 

Martiza's PIN must therefore be  3137

Answer 2

31 x 37 = 1147

Double check: Yes 1147 is in between 1000 and 1500 so her pin is "1147"

Answer 3

101 x 103 = 10403

 

How I did it: 1000 = 100 x 100, so my numbers are bigger than 100, but not much bigger.