Can someone check if I answered these two questions correctly:
- An unanswered question is whether there are infinitely many primes that are $1$ more than a power of $2$, such as $5=2^2+1$. Find two more of these primes: $$4^2+1=17, 6^2+1=37$$
- A more general conjecture is that there exist infinitely many primes of the form $n^2+1$. Exhibit five more primes of this type: $$10^2+1=101, 14^2+1=197, 20^2+1=401, 24^2+1=577, 26^2+1=677$$