Solution
= Solution
{c}
If the complete list of <prime numbers> were $p_1,\ldots,p_k$, then $N=p_1\cdots p_k+1>1$ would have a prime divisor by the <fundamental theorem of arithmetic>. No $p_i$ divides it, since $N\equiv1\pmod{p_i}$. This contradicts completeness of the list. Hence \b[there are infinitely many prime numbers].