Problem 3. It is conjectured that 2 is a primitive root for infinitely many primes p but no one can prove this! This is a special case of Artin's primitive root conjecture. The following real number is known as Artin's constant #{ PS 2 is a primitive root mod p } A := lim Estimate the value of Artin's constant numerically by computing the quotient appearing above for x-10% for k-1. 2.3.4.5.6. T and cast- ing it to a real number. Problem 4. You are carrying out a Diffie-Hellman key exchange. You and Bob agree on the (public) values of p and g, where p is a large prime and g -216 + 1 65537. You generate the secret a and Bob transmits the value of g mod p, where b is the secret generated by him. What is the shared secret s? The values of p, a, and g' mod p will be given in email Problem 3. It is conjectured that 2 is a primitive root for infinitely many primes p but no one can prove this! This is a special case of Artin's primitive root conjecture. The following real number is known as Artin's constant #{ PS 2 is a primitive root mod p } A := lim Estimate the value of Artin's constant numerically by computing the quotient appearing above for x-10% for k-1. 2.3.4.5.6. T and cast- ing it to a real number. Problem 4. You are carrying out a Diffie-Hellman key exchange. You and Bob agree on the (public) values of p and g, where p is a large prime and g -216 + 1 65537. You generate the secret a and Bob transmits the value of g mod p, where b is the secret generated by him. What is the shared secret s? The values of p, a, and g' mod p will be given in email