A Useless Recipe for Primes: A Partition-Based Algorithm for Prime Synthesis

A constructive framework for prime generation based on binary set partitions and exponent vectors. Moving beyond traditional sieving methods, this paper introduces a lateral approach to synthesize primes directly through algebraic operations. The algorithm provides new theoretical insights into the additive-multiplicative structure of integers, demonstrating that primes can be fundamentally apprehended as functions of the set of their predecessors.