Collatz Conjecture Explorer

Overview

The Collatz Conjecture Explorer allows you to test the Collatz conjecture (3n+1 problem) using Romasm assembly with BigInt support for numbers beyond JavaScript's safe integer limit.

The Collatz Conjecture

What is it?

Start with any positive integer n. Then repeatedly apply:

If n is even: n → n/2
If n is odd: n → 3n + 1

The conjecture states that every starting number eventually reaches 1, regardless of how large it is.

Status: Unproven, but verified up to ~2^71 (as of 2025).

Romasm Implementation

The explorer uses Romasm assembly to compute Collatz sequences:

; Collatz sequence in Romasm
LOAD R1, 1        ; Constant 1
LOAD R2, 2        ; Constant 2
LOAD R3, 3        ; Constant 3

loop:
  CMP R0, R1      ; Check if current number is 1
  JEQ done        ; If 1, we're done
  
  PRINT R0        ; Print current number
  
  ; Check if even (R0 % 2 == 0)
  LOAD R4, R0
  MOD R4, R2      ; R4 = R0 % 2
  CMP R4, R1      ; Compare with 1
  JEQ is_odd      ; If R4 == 1, it's odd
  
  ; Even: divide by 2
  SHR R0, R1      ; R0 = R0 >> 1 (divide by 2)
  JMP loop
  
is_odd:
  ; Odd: multiply by 3 and add 1
  MUL R0, R3      ; R0 = R0 * 3
  ADD R0, R1      ; R0 = R0 + 1
  JMP loop

done:
  PRINT R1        ; Print final 1

BigInt Support

For numbers beyond JavaScript's safe integer limit (2^53), the explorer uses BigInt arithmetic:

Numbers are stored as strings
Operations are performed digit-by-digit
Allows testing numbers with hundreds of digits

Using the Explorer