Twin Primes Explorer - Documentation

Overview

The Twin Primes Explorer searches for pairs of prime numbers that differ by exactly 2 (e.g., 11 and 13, 17 and 19). All prime checking is performed using Romasm assembly.

The Twin Prime Conjecture

What is it?

Twin primes are pairs of prime numbers that differ by 2. Examples include:

(3, 5)
(11, 13)
(17, 19)
(29, 31)

The Twin Prime Conjecture states that there are infinitely many twin prime pairs.

Status: Unproven, but bounded gaps between primes have been proven. The largest known twin primes have over 200,000 digits.

Romasm Implementation

The explorer uses Romasm assembly to check for primality:

; Check if a number is prime (simplified)
; Input: R0 = number to check
; Output: R0 = 1 if prime, 0 if not

LOAD R1, 2        ; Start checking from 2
LOAD R2, 1        ; Constant 1

check_loop:
  MUL R3, R1, R1  ; R3 = divisor²
  CMP R3, R0      ; Compare with number
  JGT is_prime    ; If divisor² > number, it's prime
  
  MOD R4, R0, R1  ; R4 = number % divisor
  CMP R4, 0       ; Check if divisible
  JEQ not_prime   ; If divisible, not prime
  
  INC R1          ; Try next divisor
  JMP check_loop

is_prime:
  LOAD R0, 1      ; Return 1 (prime)
  RET

not_prime:
  LOAD R0, 0      ; Return 0 (not prime)
  RET

BigInt Support

The explorer supports BigInt for searching very large twin prime pairs:

Can search ranges with hundreds of digits
Uses efficient prime checking algorithms
Displays twin pairs as they're found

Using the Explorer

Enter a starting number (or range)
Click "Search for Twin Primes"
View twin prime pairs as they're discovered
See statistics about the search