Numerisect¶
Numerisect is a local workbench for integer factorization, primality, prime exploration and analytic number theory. It runs on your machine, listens only on loopback, and keeps every calculation, log and result there.
Current release: 0.13.0
Numerisect is an experimental, source-distributed pre-release. The current interface contains 139 Prime Tools pages, 22 zeta/L-function pages, an expert factorization workspace, and 212 documented API operations. Start with the capability index when you know the question but not the tool name.
It is a user interface over existing number-theory libraries. PARI/GP, FLINT/Arb, YAFU, Msieve, CADO-NFS, GMP-ECM, primesieve and primecount perform the mathematics. Where no library provides a routine, a small compiled C program fills the gap. Python handles validation, process orchestration and the HTTP API; JavaScript draws the interface. Neither computes a mathematical result.
That constraint is the reason this documentation exists in the form it does. If you want to know how a result was obtained, the answer is always a named routine in a named library, and every page here says which.
The public project address is https://numerisect.com. It permanently redirects here, to the canonical documentation site at https://docs.numerisect.com, so both addresses lead visitors to the same maintained content.
Start here¶
-
New to Numerisect
Install it, factor your first integer, and learn your way around the interface.
-
Understand the results
What "proven", "probable" and "inconclusive" mean here, and why the distinction is enforced everywhere.
-
Learn the mathematics
The theory behind every tool: primality, factorization, distribution, modular structure, quadratic forms and zeta.
-
Look something up
Every HTTP route, the command line, configuration and output formats.
-
Survey the whole workbench
A compact, auditable map of the factorization, Prime Tools, zeta, verification and workflow capabilities currently shipped in 0.13.0.
What it does¶
| Area | Examples |
|---|---|
| Factorization | Automatic YAFU-to-CADO routing, SQUFOF, resumable ECM campaigns, SIQS and NFS with expert parameters, GGNFS siever diagnostics, distributed CADO-NFS, RSA Challenge verification, Mersenne trial factoring without constructing \(2^p-1\), staged Mersenne cofactor hunts, NFS polynomial selection as its own job, CADO-NFS run one workflow stage at a time, a drawn factor tree with every cofactor proven by PARI/GP, Coppersmith recovery of a factor from its leading bits, and CFRAC, Lehman and Hart |
| Primality | Rigorous proofs from two independent provers (PARI isprime and YAFU APR-CL), Baillie–PSW, a comparison laboratory across eight tests, deterministic Miller–Rabin witness sets, Pocklington and Pratt certificates, and Mersenne verdicts cross-checked across unrelated Lucas–Lehmer implementations |
| Prime structure | A 56-class catalogue, exact reciprocal periods, Gaussian and Eisenstein primes, special families, Cunningham chains, covering sets, and constrained generation |
| Distribution | Exact \(\pi(x)\) to \(10^{31}\), six mathematically distinct primecount algorithms plus independent PARI and primesieve cross-checks, nth-prime bounds, prime races, maximal gaps, and clearly labelled Hardy–Littlewood and Bateman–Horn predictions |
| Algebra | Congruences over composite moduli, four discrete-logarithm algorithms, finite fields, number fields with prime-ideal decomposition, Chebotarev experiments |
| Quadratic forms | Reduction, composition, class groups, Pell equations and continued fractions at unlimited digit length |
| Zeta and L-functions | Rigorous \(\zeta(s)\) enclosures, certified critical-line zeros, Turing counts, Riemann–Siegel, pair correlation, Dirichlet L-functions, Dedekind zeta |
| Visualization | Ulam, Sacks and polar spirals, Eisenstein lattices, modular wheels, residue heatmaps, sieve animations |
| Research workflow | Batch import, local result cache, saved workspaces, searchable reports and jobs, resource limits, CLI/API parity, export formats, and reproducibility manifests |
How results are labelled¶
Numerisect never blurs the strength of a claim. Four labels appear throughout the application and this documentation.
proven
A mathematical proof. PARI's isprime returns one; so does a verified primality
certificate. If Numerisect says proven, a proof exists.
probable A strong probabilistic test passed, most often Baillie–PSW. No counterexample is known. That is not the same as no counterexample existing.
inconclusive A timeout, a search bound, or an open question. This is never reported as a negative result. An exhausted search does not mean the thing does not exist.
exploratory A plot sample, a midpoint of a rigorous enclosure, or a heuristic estimate. Useful for seeing shape; not a certified value.
Honest limits¶
This is an experimental pre-release
Numerisect is source-distributed and has no official binary packages. It has been exercised on Fedora Linux x86-64 and by GitHub Actions on Ubuntu Linux x86-64 and ARM64, Ubuntu 24.04 x86-64 inside Windows WSL, and macOS on ARM64 and Intel. Native Windows remains unsupported, and the Arch Linux installer path has not yet received clean-host CI verification.
Some things it deliberately does not do:
- Ordinary calculations stay local. The three network-capable paths are confirmed engine source builds, optional catalogue lookups, and deliberately configured distributed CADO-NFS. Each is off by default or requires explicit authorization; there is no telemetry, analytics, or update check.
- It is not audited cryptographic software. The prime-construction laboratory is labelled experimental and should not be used to generate keys.
- It does not claim more than it proves. Where an engine cannot answer, the gap is reported rather than approximated.
Source code¶
Numerisect is free software. The complete source, including every PARI/GP program and C helper described in this documentation, is public.
-
Repository
Read the source, the commit history and the test suite.
-
Releases
Tagged versions, each with a changelog entry.
-
Report a problem
A wrong answer, a build failure or a gap in these pages.
-
Contribute
The native-computation policy every change has to satisfy.
If you report a wrong mathematical result, include the exact input, the engine that
produced it and the saved report from your output/ directory. Those three things make
the result reproducible, which is the only way a disagreement gets settled.
Licence and provenance¶
Numerisect is licensed GPL-3.0-or-later. The native engines it builds are pinned to
immutable upstream commits recorded in engine_manifest.toml, and every completed
factorization carries a reproducibility manifest listing the commands, engine revisions
and executable checksums used.