So we have $q = 311$, $p = 163$, $e = 101$, I found $d = 39281$ using Euclidean Algorithm and checked by encrypting and decrypting a message.

Next it is asking if $e = 101$ was a good choice or would the value $e = 9131$ be better.

What I know:

• $101$ = prime

• $39281$ = not prime ( $23 x\times 397$)

Both options for $e$ are relatively prime to $(p - 1) \cdot (q - 1)$ and both options for $e$ satisfy $𝑒 < λ(n)$.

Are there any other things I need to consider for $e$ to answer the question? I have looked around the forum and web but I'm stuck right now.

Hints preferred not a full answer!