Guoqing Xu

Maximum-Entropy Spacings and Hierarchical Dilution of Prime Constellations

We report a high-precision phenomenological study of the spacing statistics of prime constellations (twin primes, prime triplets, quadruplets, and higher admissible tuples) up to 1.1×108 , with a replication window at 1010. Five structures emerge. (i) A provable residue class loc...

A random anchored sieve ensemble: exact expectation and variance theorems with a complete decomposition of the variance

We introduce a probability model for sieve problems in which the sieve con straints, rather than the integers, are randomized: for every odd prime p ≤ z an anchor cp ∈ Z/pZ is drawn independently and uniformly, and we count the members of a fixed survivor set S0 that avoid every...

A random anchored sieve ensemble: exact expectation and variance theorems with a complete decomposition of the variance

We introduce a probability model for sieve problems in which the sieve con straints, rather than the integers, are randomized: for every odd prime p ≤ z an anchor cp ∈ Z/pZ is drawn independently and uniformly, and we count the members of a fixed survivor set S0 that avoid every...

Maximum-Entropy Spacings and Hierarchical Dilution of Prime Constellations

We report a high-precision phenomenological study of the spacing statistics of prime constellations (twin primes, prime triplets, quadruplets, and higher admissible tuples) up to 1.1×108 , with a replication window at 1010. Five structures emerge. (i) A provable residue class loc...