Complex sentence: The gist of the following elementary but involved proof by contradiction is due to Paul Erdős; the basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough.
Split into simpler sentences: The gist of the following elementary but involved proof is due to Paul Erdős. The basic idea of the proof is to show that a certain binomial coefficient needs to have a prime factor within the desired interval in order to be large enough.