MAX

MAX Prime Theory & MX²

Mathematical research, public materials and verifiable containers.

MAX Prime Theory is the mathematical root of the MAX method: independent research on prime numbers, deterministic structures and ordered candidate families.

MX² is a separate technical component: a portable and verifiable container format connected to protected material and practical MAX architecture.

MAX Prime Theory

A mathematical research path focused on deterministic structure, modular organization and reproducible inspection.

The mathematical root of the MAX method

MAX Prime Theory started from a simple question: can ordered structure be found inside a domain that usually appears irregular?

The research studies deterministic paths for prime candidates, using arithmetic structure and modular filters. The purpose of this page is not to reproduce the mathematics. Formulas, proofs, experimental details and numerical results belong in the public papers, demos and experimental material.

One important experimental theme is enrichment: filtered candidate families can show a higher observed density of prime hits than a simple classical baseline would suggest. This does not replace a proof and does not turn the theory into cryptography, but it explains why the public Challenge is meaningful at larger computational scales.

Inside the MAX ecosystem, the correct connection is conceptual and structural: MAX Prime Theory inspired the idea of an identity built from an ordered local process, not from a username, password or server-created account.

Open MAX Prime Challenge

Relationship with MAX

The theory inspired the identity model. It does not replace established cryptography.

π
Research

Mathematical structure

MAX Prime Theory belongs to the mathematical layer of the project. It studies deterministic structure, modular filters and public research material.

ID
Identity

MAX ID model

The theory helped shape the idea of a local identity represented by a public, verifiable root. This connects naturally with hashes, Merkle roots and proof objects.

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Boundary

Not new cryptography

MAX Prime Theory is not an encryption algorithm, not a signature scheme and not a replacement for SPHINCS+, FrodoKEM, Argon2id, hashes or public-key verification.

Public papers and experimental material

These Zenodo records contain mathematical details, definitions, experimental work, numerical material and technical development of MAX Prime Theory.

EXP
Zenodo data

Experimental data and enrichment

Supplementary experimental data, numerical tables and computational parameters related to the observed enrichment and reproducibility of MAX Prime Theory experiments.

Open experimental data on Zenodo
P1
Zenodo paper

Index pre-sieve and local factors

Introduces affine-related quadratic polynomials, an index pre-sieve and finite truncations of Bateman–Horn local factors as an experimental study.

Open Paper 1 on Zenodo
P2
Zenodo paper

Uniform modular partition

Develops the modular partition of prime candidates for a pair of affine-correlated quadratic polynomials based on the index pre-sieve.

Open Paper 2 on Zenodo
P3
Zenodo paper

Parametric family

Extends the framework to a parametric family of affine-related quadratic polynomials, modular partitions and Bateman–Horn classes.

Open Paper 3 on Zenodo
CH
Public client

MAX Prime Challenge

Public distributed search for large probable primes using the structured path developed in MAX Prime Theory. The local mode can also be used to inspect behavior.

Open MAX Prime Challenge

Public demos on Hugging Face

These demos are interactive inspection tools. They are useful for comparing Sequence-A behavior with and without modular filters and for exploring how modular choices affect the generated candidate families.

A
Baseline

Sequence-A without filters

Baseline demo for Sequence-A without additional modular filters. Useful as a reference point before comparing filtered variants.

Open demo
3
Modulo filter

Sequence-A modulo 3

Demo focused on the effect of a modulo 3 filter. It helps isolate one modular layer of the candidate-selection process.

Open demo
7
Modulo filter

Sequence-A modulo 7

Demo focused on the effect of a modulo 7 filter. It provides another independent modular comparison.

Open demo
3+7
Combined filters

Sequence-A modulo 3 + 7

Demo for a combined modular-filter configuration. Useful for observing how multiple modular constraints interact.

Open demo
3–37
Extended filters

Sequence-A moduli 3 to 37

Demo for a broader modular configuration excluding 5. It is meant for deeper inspection of filtered candidate families.

Open demo
MAX
Test space

MAX-Test

Public test/demo space connected to the MAX research and verification path. It may sleep when inactive, as Hugging Face Spaces often do.

Open MAX-Test

MX²

MX² belongs to the practical side of MAX: a portable and inspectable container for protected material.

A verifiable container, not a new cryptography

MX² is a portable, password-protected container format designed to protect long-term high-entropy secrets in a small, inspectable and reproducible way.

It is based on known and studied components, including Argon2id and XChaCha20-Poly1305. Its value is not a claim of proprietary cryptography, but a clear format that can be read, implemented, tested and reviewed.

In the MAX ecosystem, MX² is connected to protected local material and practical identity recovery. It does not replace signatures, hashes, authenticated encryption, key derivation or post-quantum components.

View MX² on GitHub

What this page does not claim

This distinction is important for mathematicians, cryptographers, engineers and future technical review.

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Boundary

Not a security claim

The existence of MAX Prime Theory does not prove that MAX App or MAX IoT are secure. Operational security must be evaluated through the actual components, implementations, flows, keys, signatures, hashes, server behavior and review process.

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Correct reading

Research and architecture

MAX Prime Theory is research. Observed enrichment is an experimental result, not an operational security guarantee. MX² is a technical container. MAX App and MAX IoT use known cryptographic components inside a MAX-specific architecture oriented to identity and verification.

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