Primes in Duodecimal

In the duodecimal (base-12) framework, prime numbers reveal a deeper structural harmony that decimal obscures. Because 12 = 2^2 x 3, the duodecimal base shares factors with far more natural ratios than decimal. Why Base-12 Reveals Prime Patterns In base-12, the first few primes are written: 2, 3, 5, 7, E (=eleven), 11 (=thirteen), 15 (=seventeen), 17 (=nineteen)... A prime p greater than 3 must end in 1, 5, 7, or E in base-12 (since it cannot be divisible by 2 or 3). This reduces candidates by two-thirds. The Dozen-Prime Theorem For any prime p > 3 expressed in base-12: - p = 1 mod 12: twin-prime candidate with p+2 - p = E mod 12: twin-prime candidate with p-2 This symmetry around the dozen shows that twin primes cluster around multiples of 12. Sieve of Eratosthenes in Base-12 All composites divisible by 2 end in: 0, 2, 4, 6, 8, X All composites divisible by 3 end in: 0, 3, 6, 9 Primes above 3 must end in: 1, 5, 7, E This natural 4-residue structure makes base-12 optimal for prime arithmetic.