MAX Prime Challenge

A public mathematical experiment comparing structured prime search with the classical random baseline.

MAX Prime Challenge does not simply ask whether another large probable prime can be found. It asks whether the structured candidate path developed in MAX Prime Theory can reach one with fewer candidate-testing operations than simple random generation would predict.

Every official Challenge is therefore a measurable experiment. Before the search begins, the classical reference is known: the average candidate count and the probability of finding at least one prime within the planned limit. When a verified hit is found, the observed result is compared with that same reference.

The complete comparison is public: live progress, classical expectation, observed position, formulas, candidate data and independent reproduction instructions. The purpose is not to ask for trust, but to make the experiment inspectable and repeatable.

Open GitHub repository Official Results

Why this Challenge exists

To test a precise question: can a structured search outperform the classical random baseline?

A different question from an ordinary prime search

Most large-prime projects ask whether another large prime can be found. MAX Prime Challenge asks an additional and measurable question: whether a structured mathematical path can find large probable primes more efficiently than the classical expectation for random integers of comparable size.

The classical model gives a reference before any computation begins. For numbers of a given size, it estimates the average number of random candidates required to encounter a prime and the probability of finding at least one prime after a chosen number of tests.

The Challenge then performs the structured search and records what actually happens. If the first verified probable prime appears before the classical average, the reduction in required candidate-testing operations can be measured directly. If no hit appears, that result is also visible and remains part of the experiment.

Larger experiments require substantial computation, so the search is divided into official work units processed by multiple computers. Distribution makes the scale possible; the real purpose remains the mathematical comparison.

Every official Challenge follows the same sequence: publish the reference, run the search, verify any hit, compare prediction with observation, and release enough data for independent reproduction.

MAX Prime Theory & MX²

What makes the Challenge different

It does not publish only a prime: it publishes the prediction, the observation and the comparison.

From classical expectation to observed result

MAX Prime Challenge uses deterministic candidate families and modular filters derived from MAX Prime Theory. The resulting sequence is not a random sample of all integers: it is a reproducible path that can be generated again from the same published parameters.

For every official run, the Results page shows the classical average first-prime position, the probability of already having found at least one prime at the current or winning point, and the probability within the full planned limit.

When a verified hit is found, its actual position is divided into the classical average. This does not claim that primes become intrinsically more probable everywhere. It measures how many fewer candidate-testing operations that specific structured Challenge required compared with the classical average for random integers of similar size.

Repeating the same comparison at different scales is the core of the project. A single result may be fortunate; a persistent pattern across independent Challenges is scientifically more interesting. For that reason, successful and unsuccessful runs must both remain public.

Local Mode lets anyone inspect the candidate path directly. Official Mode extends the same process into a coordinated distributed experiment with server-assigned work and verified results.

Read MAX Prime Theory & experiments Experimental data on Zenodo

How participation works

Receive work, compute locally, submit the result.

Challenge

Official work is divided

The official server defines a Challenge and divides the search into work units. Each unit represents one portion of the larger computation.

Client

Your computer works locally

The client receives a work unit, performs the computation on your computer and tests the assigned candidates.

Result

The result is submitted

If an interesting result is found, the client submits it to the official server so it can be recorded as part of the Challenge.

Local mode and official mode

The client can be used for local testing or for official participation.

Local mode

Test on your computer

Local mode is for testing and inspection. It lets users run local checks on their own computer without joining official work.

Official mode

Contribute to the Challenge

Official mode connects the client to the MAX Prime server, receives official work units and submits results under a MAX identity.

Registration through MAX ID

Official participation uses a MAX identity, not the classic email + password model.

A mathematical identity inside the MAX model

Official participation does not start from a traditional account based on email, password and personal-data profiling.

In this context, MAX ID is not a civil identity document, not an email account and not a profile built from personal information.

MAX ID is the public verifiable root of a MAX identity: a mathematical and deterministic identity object used to attribute work and results inside the MAX model.

This allows the Challenge to connect public contribution, local computation and verifiable identity without making personal identification the center of the system.

The deeper identity model is described in the MAX App, MAX Prime Theory and Technical Verification pages.

MAX App MAX Prime Theory & MX² Technical Verification

Public client on GitHub

The Challenge is source-first: the public client can be inspected, built and run.

GUI

Recommended

Graphical interface

The GUI is the recommended way to participate because it makes the process easier to follow: registration state, local mode, official mode and results are visible in one place.

CLI

Technical users

Command-line interface

The CLI is available for users who prefer terminal workflows or want a more direct path to inspect and run the client.

Source-first distribution

The public repository contains the Rust source code for the client, the GUI and CLI entry points, configuration material and project documentation.

Technical users can clone the repository, read the code, build the project and run the client. This page does not claim that universal installers are already available.

The repository contains the public client. Private server infrastructure and administrative tools are not part of the public client repository.

Open MAX Prime Challenge on GitHub

Verify the results yourself

MAX Prime Challenge does not ask you to trust a result without checking it.

Reproduce a published result on your own computer

Every official result can publish the mathematical values needed to reconstruct the same candidate independently: the starting value, step, iteration, CRT filter, candidate size and SHA-256 fingerprint.

Download the public Rust client from GitHub, open Local Mode and copy the values published on the Official Results page.

To reproduce only the winning candidate, use the published n_raw value as the local starting value, keep the published CRT modulus M and remainder R, select one iteration and test N.

The client should generate a probable prime with exactly the same number of digits and exactly the same SHA-256 shown on the website.

This means that the public result is not only displayed: it can be reproduced independently using the public source code.

Open verification data Download the public client

Probable primes

The language is important: the Challenge searches for probable primes.

Not definitive prime certification

MAX Prime Challenge searches for probable primes.

The client uses probable-primality testing, including Miller-Rabin. For this reason, hits should be communicated as probable primes.

A definitive mathematical certification would require a separate and explicitly declared process.

Official results

The Results page is the public experimental record: reference, progress, outcome and verification.

Prediction, observation and independent verification

While a Challenge is active, the Results page shows what simple random generation would predict: the classical average first-prime position, the probability accumulated so far and the probability available within the full planned search limit.

After an official hit, the page records the exact candidate position, its size, the work unit, the SHA-256 fingerprint, the public MAX identity when available, and the observed reduction in candidate-testing operations relative to the classical average.

The latest verified result is shown as the main case study. Earlier results move automatically into the historical table, preserving a growing sequence of comparable experiments across different numerical scales.

This page explains why the experiment exists. The Results page shows whether the structured search actually did better, worse or exactly as the classical reference would suggest.

Open Official Results GitHub Repository MAX Prime Theory & MX²