TITLE: Sum of reciprocals of primes
QUESTION [9 upvotes]: If $p_i$ is an infinite set of distinct primes such that $c=\sum\frac{1}{p_i} < \infty$, must $c$ be a transcendental number?

REPLY [14 votes]: No. Pick any positive algebraic number, and by choosing your primes carefully, you can make the infinite series converge to your number.