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Martin Sleziak
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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.

As for GRH, the prettiest one I know is this complete solution of the odd Goldbach conjecture (that every number greater than 5 is a sum of 3 primes).

As for GRH, the prettiest one I know is this 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.

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Igor Pak
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As for GRH, the prettiest one I know is this complete solution of the odd GoldbackGoldbach conjecture (that every number greater than 5 is a sum of 3 primes).

As for GRH, the prettiest one I know is this complete solution of odd Goldback conjecture (that every number greater than 5 is a sum of 3 primes).

As for GRH, the prettiest one I know is this complete solution of the odd Goldbach conjecture (that every number greater than 5 is a sum of 3 primes).

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Igor Pak
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As for GRH, the prettiest one I know is this complete solution of odd Goldback conjecture (that every number greater than 5 is a sum of 3 primes).