MATH 319 Primality Testing

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In this exercise you will be using Maple to discover whether or not certain numbers are primes. You could do this easily with the Maple function isprime but that is not the point of this exercise. Instead you should determine the answers to the following questions using the modp function:

1. Is the given number a probable prime to base a where a is 2, 3, 5, 7, 11, or 13.

2. If it is a probable prime to base a, then determine if it is a spsp(a) using the strong pseudoprime test outlined in class.

3. Using the fact that the smallest number which is spsp(2) and spsp(3) at the same time is 1,373,653 determine which of the given numbers are primes.

The numbers to test:

88357, 93961, 90749, 90751, 97567

101101, 101107, 188461, 188473, 1082809

For each of these numbers and for each base 2, 3, 5, 7, 11, and 13 answer questions 1 and 2. Then answer question 3. Clearly indicate what led you to the answers you have given. For example, determine if 88357 is a probable prime to base 2. If it is then apply the strong pseudoprime test. Move to base 3. Continue through the bases and then answer question 3 – is 88357 a prime?

Recall that modp(a$^k,m); is the Maple syntax for