What is the greatest prime number less than 8,073? What is the least prime number greater than 8,073?

There's no simple formula for primes, so the only way to do it is to either test numbers above and below 8073 until you get a prime, or generate all primes up to something above 8073, or look them up. That's work you can do.

8072 is even, not prime. You can skip all even numbers, or numbers with digits adding to something divisible by 3, or ending in a 5.
8071 has 7 as a factor
8069 is the next one to try.

Divide n by primes until you get to √n. You don't have to go past that, because any factor greater than √n would have to be matched to a factor less than √n.

1) 8069
2) 8081

http://www.wolframalpha.com/input/?i=primes+between+8000+and+8100

Pick both answers from this list.

The "work" consists of typing the query into the window. The actual method would be to run a Sieve algorithm using the primes up to the square root of 8073.
sqrt(8073) is about 89, which means you'd have to do trial division by all the primes up to 89:
http://www.wolframalpha.com/input/?i=primes+%3C+90