SOLUTION: Use primality testing to determine if the natural numbers are prime or composite. Show all steps. here are the numbers 271, 319, 731, and 1801

We only need to try dividing a number by primes not exceeding the square root 
of the number.
------------------------
271:
=16.4... 
We know it isn't divisible by 3 because the sum of its digits is not a multiple
of 3.  It doesn't end in 5 or 0 so it is not divisible by 5.  We try 7. Nope
We try 11.  Nope.  We try 13.  Nope.  So it's prime because the next prime
is 17, which is more than 16.4. 

271 is prime
------------------------
319:
=17.86... 
We know it isn't divisible by 3 because the sum of its digits is not a multiple
of 3.  It doesn't end in 5 or 0 so it is not divisible by 5.  We try 7. Nope
We try 11.  Yep!  319 = 11*29. So 319 is composite.

319 is composite.
------------------------
731:
=27.037... 
We know it isn't divisible by 3 because the sum of its digits is not a multiple
of 3.  It doesn't end in 5 or 0 so it is not divisible by 5.  We try 7. Nope
We try 11.  Nope.  We try 13.  Nope.  We try 17. Yep!  731 = 17*43. So 731 is
composite.

731 is composite.
------------------------ 
1801:
sqrt(1801)=42.4...

We know it isn't divisible by 3 because the sum of its digits is not a multiple
of 3.  It doesn't end in 5 or 0 so it is not divisible by 5.  We try 7. Nope
We try 11.  We try 13.  Nope. We try 17. Nope. We try 19. Nope. We try 23.
Nope. We try 29.  Nope. We try 31.  Nope. We try 37.  Nope. We try 41.  Nope. So
it's prime because the next prime is 43, which is more than 42.4. 

1801 is prime

Edwin