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.
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.
Start here¶
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New to Numerisect
Install it, factor your first integer, and learn your way around the interface.
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Understand the results
What "proven", "probable" and "inconclusive" mean here, and why the distinction is enforced everywhere.
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Learn the mathematics
The theory behind every tool: primality, factorization, distribution, modular structure, quadratic forms and zeta.
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Look something up
Every HTTP route, the command line, configuration and output formats.
What it does¶
| Area | Examples |
|---|---|
| Factorization | Automatic YAFU-to-CADO routing, SQUFOF, resumable ECM campaigns, SIQS and NFS with expert parameters, cross-engine verification, distributed CADO-NFS |
| Primality | Rigorous proofs, Baillie–PSW, a comparison laboratory across eight tests, deterministic Miller–Rabin witness sets, Pocklington and Pratt certificates |
| Prime structure | A 56-class catalogue, reciprocal periods, special families, Cunningham chains, covering sets, constrained generation |
| Distribution | Exact \(\pi(x)\) to \(10^{31}\), six independent counting algorithms compared, nth-prime bounds, prime races, maximal gaps, 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, continued fractions of quadratic irrationals |
| 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 |
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. Windows WSL and macOS paths are implemented but have not been verified by the project.
Some things it deliberately does not do:
- It does not go online during calculations. Engine installation and the optional catalogue lookups are the only outbound paths, both behind explicit confirmation.
- 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.
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Repository
Read the source, the commit history and the test suite.
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Releases
Tagged versions, each with a changelog entry.
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Report a problem
A wrong answer, a build failure or a gap in these pages.
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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.