Goldbach Conjecture Explorer

Overview

The Goldbach Conjecture Explorer verifies that every even integer greater than 2 can be expressed as the sum of two prime numbers. All computations are performed using Romasm assembly.

The Goldbach Conjecture

What is it?

The Goldbach Conjecture (strong form) states:

Every even integer greater than 2 can be expressed as the sum of two primes.

Examples:

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 = 5 + 5
12 = 5 + 7

Status: Verified up to ~4×10¹⁸, but unproven for all even numbers.

Romasm Implementation

The explorer uses Romasm assembly to find prime decompositions:

; Find two primes that sum to an even number
; Input: R0 = even number
; Output: R1, R2 = two primes that sum to R0

LOAD R1, 2        ; Start with smallest prime (2)

try_prime:
  ; Check if R1 is prime (using prime check function)
  CALL is_prime
  CMP R0, 1
  JNE next_prime  ; If not prime, try next
  
  ; Calculate R2 = R0 - R1
  LOAD R2, R0
  SUB R2, R1
  
  ; Check if R2 is prime
  LOAD R0, R2
  CALL is_prime
  CMP R0, 1
  JEQ found       ; If R2 is prime, we found a solution
  
next_prime:
  INC R1
  CMP R1, R0
  JLT try_prime   ; Continue searching
  
found:
  ; R1 and R2 are the two primes
  RET

BigInt Support

The explorer supports BigInt for testing very large even numbers:

Can test numbers with hundreds of digits
Finds multiple decompositions when they exist
Uses efficient prime generation and checking

Using the Explorer