Lapbertrand May 2026

The result: For any integer ( n > 10^6 ), LAPBERTRAND locates a prime in the interval

We state the : For sufficiently large (n), there exists a prime (p) such that [ n < p \le n + \lfloor \sqrt{n} \rfloor. ] Furthermore, this prime can be found in (O(\log^2 n)) time using the LAPBERTRAND eigen-sieve. If true, this would reduce the prime gap bound from (n) (trivial) to (\sqrt{n}) — a near-quadratic leap. Criticisms Some number theorists remain skeptical. Dr. Elena Voss (MPI for Mathematics) notes: "LAPBERTRAND is clever engineering, but the spectral method assumes equidistribution of residues in a way that’s not proven. They’re essentially guessing where primes should be, then verifying. That’s not a constructive proof — yet." Nevertheless, the open-source implementation (C++/CUDA, available on GitHub) has already been used to discover 12 new record prime gaps below (2^{64}). Conclusion Whether or not LAPBERTRAND holds asymptotically, it has already changed how we search for nearby primes. The old Bertrand guard — "there is a prime within a factor of 2" — now seems almost lazy. We are lapping it. LAPBERTRAND

Bertrand’s postulate gave us existence. LAPBERTRAND gives us location. The result: For any integer ( n &gt;