divisor-function

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zfifteen / prime-gap-structure

Investigates deterministic prime-gap interiors using the Divisor Normalization Identity (DNI). Establishes the Gap Winner Rule (GWR) the raw-Z maximizer is always the leftmost min-d(n) carrier. Validates the No-Later-Simpler-Composite Theorem with zero violations through 10^18. Documents hierarchical first-arrival laws and square-phase terminal.

number-theory gwr computational-number-theory analytic-number-theory prime-gaps divisor-function gap-winner-rule prime-gap-structure divisor-normalization-identity no-later-simpler-composite-theorem prime-placement prime-squares hierarchical-first-arrival square-phase-closure raw-z-maximizer dn-minimization

Updated Sep 6, 2026
Python

Osman209 / prime-number-studies

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Independent re-derivations, measurements and negative results around the division table — with runnable verification code. No RH claims.

reproducible-research open-science prime-numbers riemann-zeta number-theory sieve-of-eratosthenes sieve-of-sundaram divisor-function

Updated Sep 8, 2026
Python

jorgell23-sys / prime-abundant-enumeration

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The n with rad(n) | sigma(n) (OEIS A175200) listed without sieving, to 10^13: 85,695 terms where the published b-file has 10,000. Includes the counts of prime-perfect numbers to 10^13 and six invariants that do not predict the size of these sets.

oeis number-theory computational-number-theory arithmetic-functions perfect-numbers divisor-function

Updated Sep 10, 2026
Python

zfifteen / cognitive-distortion-layer

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Validated curvature signal for integer structural classification. κ(n) = d(n)·ln(n)/e² separates primes from composites at 3.05× ratio with 88.2% hold-out accuracy. Core signal layer of the Z Framework. Includes CDL API, adaptive threshold protocol, Z-normalization, and falsification experiments. Active research: v-inference.