As for GRH, the prettiest one I know is thisthis complete solution of the odd Goldbach conjecture (that every number greater than 5 is a sum of 3 primes).
Deshouillers, J.-M.; Effinger, G.; te Riele, H.; Zinoviev, D., A complete Vinogradov 3-primes theorem under the Riemann hypothesis, Electron. Res. Announc. Am. Math. Soc. 3, 99-104 (1997). ZBL0892.11032.