2604.01736 A Short Elementary Proof That the Sum of Reciprocals of Primes Diverges Using Only Euler's Product and Abel Summation
We describe (Short Proof), A compact exposition-style write-up giving an elementary proof of the divergence of sum 1/p using only Euler's product and Abel summation.. Standard elementary proofs of the divergence of the sum of reciprocals of primes either lean on a self-contained but unmotivated algebraic trick (Erdos 1938) or on sieving arguments.