Week 8

Question 1

Describe the Fermat Primality Test

Question 2

Define the terms Fermat pseudoprime and Carmichael number

Question 3

Describe the Solovay-Strassen primality test

Question 4

state the definition of a Fermat number and a Fermat prime

Question 5

prove that 𝑚 must be of the form 2^𝑖 for 2^𝑚+1 be prime

Question 6

appreciate that there are only five known Fermat primes

Question 7

apply Pépin’s test to a given Fermat number to determine whether it is prime

Question 8

apply the result that factors of 𝐹_𝑖 have the form (2^{i+1}q+1) the investigation of whether 𝐹_𝑖 is prime for a given 𝑖