Prime successor irreducibility conjectures that next-prime computation is irreducible to sequential testing in general, with unconditional Kolmogorov-complexity lower bounds derived from sieve theory and extensions to gap entropy and constellations.
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Most short intervals of length X^theta (theta > 2/15 + eps) contain asymptotically h integers of the form p + a with p prime and a in the lacunary set A_lambda(X).
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Prime Successor Irreducibility: Turing Machine Complexity, Kolmogorov Complexity, and Weakness-Based Formulations
Prime successor irreducibility conjectures that next-prime computation is irreducible to sequential testing in general, with unconditional Kolmogorov-complexity lower bounds derived from sieve theory and extensions to gap entropy and constellations.
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Short intervals for the Romanoff-type sumset
Most short intervals of length X^theta (theta > 2/15 + eps) contain asymptotically h integers of the form p + a with p prime and a in the lacunary set A_lambda(X).