Exercises

1) Write a new version of goodprime which uses the criteria that p is a good prime if (p-1) has a prime factor exceeding p/(log_2(p)). Use ifactors().

2) Examine the asymptotics of good primes: Write a procedure that will test what proportion of primes in the range 2^i....2^(i+1) are good, as i varies. Graph the result.

3) Create a finite field of 7^2 elements. Try to find all of the primitive elements. There should be

phi(49-1) = 16;