Ivan Anisenya

Dickson's conjecture versus superadditivity of prime-constellation counts: explicit certificates, the exact twin-prime crossing, and a registry of incompatible conjectures

Hensley and Richards (1974) showed that the prime k-tuples conjecture contradicts the Hardy-Littlewood inequality pi(x+y) <= pi(x)+pi(y). This note records the same incompatibility for constellation counting functions (twin primes, cousins, sexy primes, two triplet patterns, quad...