prime-formula 0.3.0

High-performance prime number generation and constellation finding using novel wheel factorization
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# prime-formula
A Rust implementation of the Formula of Primes (FOP) using insights from the Periodic Table of Primes (PTP).

## Overview

For millennia, prime numbers have eluded precise prediction, their distribution remaining one of mathematics' 
greatest mysteries. This project implements groundbreaking research that establishes a Periodic Table of Primes 
(PTP) – a revolutionary framework for understanding prime numbers and their patterns.

### Key Theory Foundations

1. Periodic Table of Primes (PTP)
    - Built from the foundational primes 2, 3, 5, and 7
    - Identifies 48 critical integers within every 210-number cycle (2×3×5×7)
    - These 48 integers generate all primes and composites without factors of 2, 3, 5, or 7

2. Formula of Primes (FOP)
    - Algorithmically generates primes, twin, triple or higher primes
    - Reveals deterministic relationships between primes and their PTP roots

3. Counting Functions
    - Provides analytical tools for prime and twin prime distribution analysis

### Features

Rust CLI & Library Implementation

 - 🚀 Generate primes using PTP's 48-root framework
 - 🔍 Analyze twin and triple prime distributions
 - 📈 Compute prime counting functions
 - ⚡ High-performance Rust implementation for:
    - Large-number theory applications
    - Cryptographic research
    - Mathematical pattern discovery

### Installation

```commandline
# For library use
cargo init
cargo add prime-formula  
```

Will initialize a new rust project and pull in the prime-formula library.

```
# For CLI use
cargo install prime-formula
```

Will install the binary locally to get started quickly.

### Usage

```commandline
# Generate primes using prime-formula CLI
prime-formula 0 1e6
```

Will count primes in the range 0 - 1,000,000.

```commandline
prime-formula --dist 1e3 -c 2
```

Will count twin primes in the range 0 - 1,000.

```commandline
prime-formula 1e12 --dist 1e3 -p
```

Will find primes that are at least 1×10<sup>12</sup> in size with a window size of 1,000.

### Why This Matters

This implementation bridges theoretical number theory with practical computation, offering:

 - A predictive framework for prime distribution
 - New tools for twin prime conjecture analysis
 - Efficient algorithms leveraging PTP's structural insights


### References

> "Each prime is an offspring of the 48 integers on the PTP – finally giving us a periodic law for primes."

Paper: [Periodic Table of Primes (PTP) Theory](https://ssrn.com/abstract=4742238)