computational-number-theory

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.

Repository for the FermulerPy core package. Fermulerpy is useful for problems related to various fields of Number Theory.

Object-oriented continued fractions with Python.

Empirical discovery: Semaev's S₃ relation matrix over j=0 elliptic curves stabilizes at rank 3. Optimizes ECC cryptanalysis & finite-field linear algebra.

Code for the computation of paramodular forms via lattice methods

A Machine-Verified Constructive Proof of Lemoine's Conjecture.

Executable arithmetic topology: named number-theory theorems verified from scratch in C++, dual-implementation and oracle-refereed

k-tuplet-search

The Golden Ratio’s Footprint in Happy Number Sequences.

Three-square balance: record locations for the minimal spread in representations k = x² + y² + z² ::: OEIS A395008

A Formal Proof of the Irrationality of the Euler-Mascheroni Constant.

A Formal Proof of the Non-Existence of Odd Perfect Numbers for Euler Primes p ≥ 5 via Structural Divisibility Constraints.

A finite algebraic covering system for the Erdos-Straus conjecture, verified to 10^11 (max A = 359); exploratory search to 1.2x10^12 finds A = 479. Gateway decompositions via divisors of N^2.

A Formally Verified Structural Parity Proof of the Collatz Conjecture.

An algorithm that computes modular nested exponentiation efficiently.

Gap-record locations for the canonical four-square balance gap A122921(n) - ceiling(sqrt(n/4)) ::: OEIS A396760

GPU/CPU Cunningham chain search engine with interactive 2-adic visualizations and analysis tools

Bounding Singmaster's Conjecture via Constructive Type Transformation in Lean 4.

Conditional Riemann Hypothesis research atlas with public scripts, certificates, Zenodo records, and proof-audit status boundaries

This is an independent, unofficial Julia interface to PARI/GP. It is not affiliated with, endorsed by, or maintained by the PARI/GP development team.