4 papers
math.NT2026
On nonconvex constellations among primes II: (458,3240)
Fred B. Holt
Extending our work on the -tuple conjecture, we previously applied those methods to the Engelsma counterexamples (narrow constellations) of length and span . H…
math.NT2026
On nonconvex constellations among primes I
Fred B. Holt
Extending our work on the -tuple conjecture, we apply those methods to the Engelsma counterexamples (narrow constellations) of length and span . We track the e…
math.NT2026
Surviving Eratosthenes sieve I: quadratic density and Legendre's conjecture
Fred B. Holt
We have been studying Eratosthenes sieve as a discrete dynamic system, obtaining exact models for the relative populations for small gaps (currently gaps ) in the cycle o…
math.NT2025
Eratosthenes sieve supports the -tuple conjecture
Fred B. Holt
Viewing Eratosthenes sieve as a discrete dynamic system, we show that every admissible instance of every admissible constellation of gaps arises and persists in Eratosthenes sieve.…