Problem Explorers

Exploring unsolved mathematical problems with Romasm

Overview

Romasm includes interactive explorers for various unsolved mathematical problems. Each explorer uses Romasm assembly to perform computations, demonstrating the language's capabilities while contributing to mathematical research.

Available Explorers

Collatz Conjecture

The 3n+1 problem: Does every positive integer eventually reach 1?

  • Test starting numbers of any size (BigInt support)
  • View the complete sequence
  • Count steps to reach 1

Documentation | Try it

Twin Primes

Search for large pairs of primes that differ by 2.

  • Find twin prime pairs
  • Use Romasm prime checking algorithms
  • BigInt support for very large numbers

Documentation | Try it

Goldbach Conjecture

Verify that every even number > 2 is the sum of two primes.

  • Test even numbers
  • Find prime pair decompositions
  • Push verification limits

Documentation | Try it

Erdos-Straus Conjecture

Find unit fraction decompositions of 4/n.

  • Search for solutions
  • Test various values of n

Documentation | Try it

Beal Conjecture

Search for counterexamples to A^x + B^y = C^z.

  • Test various combinations
  • Use Romasm power calculations

Documentation | Try it

Legendre's Conjecture

Verify that there's always a prime between n² and (n+1)².

  • Test for various values of n
  • Find primes in the range

Documentation | Try it

Mersenne Primes

Search for Mersenne primes (2^p - 1 where p is prime).

  • Test various prime exponents
  • Check against known Mersenne primes

Documentation | Try it

Brocard's Problem

Find solutions to n! + 1 = m².

  • Test factorials
  • Check for perfect squares

Documentation | Try it

Perfect Numbers

Search for perfect numbers (sum of divisors equals the number).

  • Test various numbers
  • Calculate divisors using Romasm

Documentation | Try it

Pascal's Triangle

Generate and analyze Pascal's Triangle.

  • Calculate triangle rows
  • Count number occurrences (Singmaster's Conjecture)

Documentation | Try it

Common Features

All explorers share common features:

  • Romasm Implementation: Core computations done in Romasm assembly
  • BigInt Support: Handle numbers beyond JavaScript's limit
  • Interactive UI: Enter values and view results
  • Code Display: See the Romasm code being executed

Related Documentation