RandyMcMillan

use std::collections::HashMap;
use rand::{seq::SliceRandom, thread_rng};

// --- BQS Constants ---
// Maximum number of Byzantine faults (f or b) the system can tolerate.
const F: u32 = 4;

// The required supermajority count for a client to accept a value as correct.
// A value is only considered valid if F + 1 servers report it, allowing the
// client to mask 'F' colluding malicious responses. 

RandyMcMillan

// main.rs - A minimal Crust program with tests
//
#![cfg_attr(not(test), no_std)]
#![cfg_attr(not(test), no_main)]

extern crate libc;

#[cfg(not(test))]
use core::panic::PanicInfo;

RandyMcMillan

// --- Dependencies ---
// This simple example relies only on standard library features.
use std::error::Error;
use std::fmt;

// --- Error Handling ---

/// A simple custom error type for parsing issues.
#[derive(Debug)]
struct ParseError {

RandyMcMillan

// The core concept is that for a number 'n', if 'n % d == 0', then 'n' is divisible by 'd'.
// Divisibility tests rely on properties of the digits.

/// 🔢 Divisibility Tests Module
mod divisibility_tests {
    // Helper function to get the sum of digits
    pub fn sum_digits(n: u64) -> u64 {
        let mut sum = 0;
        let mut num = n;
        while num > 0 {

RandyMcMillan

// Verbose Script: Corrected Floating-Point Comparison

fn main() {
    // ----------------------------------------------------
    // 1. Define Constants
    // ----------------------------------------------------

    const PI: f64 = std::f64::consts::PI;
    let gamma_one_half: f64 = PI.sqrt();
    

RandyMcMillan

import secrets
from statistics import mean

# secp256k1 parameters
p = 2**256 - 2**32 - 977
b = 7  # y^2 = x^3 + 7

def is_quadratic_residue(n):
    """Return True if n is a quadratic residue mod p (including 0)."""
    if n == 0:

RandyMcMillan

import secrets

# secp256k1 parameters
p = 2**256 - 2**32 - 977
a = 0
b = 7

def random_256bit_int():
    # random 32-byte string interpreted as big-endian integer
    return int.from_bytes(secrets.token_bytes(32), "big")

RandyMcMillan

#!/usr/bin/env python3
import sys
import secrets
from statistics import mean

p = 2**256 - 2**32 - 977
b = 7  # y^2 = x^3 + 7

def is_quadratic_residue(n):
    return n == 0 or pow(n, (p - 1) // 2, p) == 1

RandyMcMillan

// a 3D Ulam Spiral 
// projected onto a 2D grid,
// marking primes with their Z-index.

/// Generates a boolean vector where `is_prime[i]` is true if `i` is a prime number (Sieve of Eratosthenes).
fn sieve_of_eratosthenes(max_value: usize) -> Vec<bool> {
    if max_value < 2 { return vec![]; }
    let mut is_prime = vec![true; max_value + 1];
    is_prime[0] = false;
    is_prime[1] = false;

RandyMcMillan

use std::fmt::{self, Display};

// Define a type alias for a binary sequence (a vector of 0s and 1s)
type BinarySequence = Vec<u8>;

/// Attempts to demonstrate Cantor's Diagonal Argument.
///
/// It generates a list of sample binary sequences and constructs a new
/// diagonal sequence that is guaranteed to not be in the list.
fn main() {