(a) Let $p$ be the prime 1073741827, with $\Bbb{F}_p$ the corresponding finite field. A primitive root in $\Bbb{F}_p$ is equal to $g=2$. Use a factor base of primes up to 13 to find the discrete logarithm of 1000173298. You should compute powers of g modulo p using Magma (or other program) and use the index calculus method.
(b) Let p be the prime 34359738421, with $\Bbb{F}_p$ the corresponding finite field. A primitive root in $\Bbb{F}_p$ is equal to $g=2$. Experiment with various factor bases to see what size factor base would likely allow you to determine the discrete logarithm of 7164430421. (You are not asked to find the discrete logarithm, unless you wish to.)