Ternary Prime Laboratory

Binary writes numbers with 0 and 1, ternary – the smallest odd base – with 0, 1 and 2. Could an odd number system reveal a structure of the primes that binary hides, and help with the prime number problem? Ternary Prime Lab turns that idea into six testable hypotheses and checks every one of them live in your browser.

It sieves the primes up to ten billion, races the primes ending in the trit 1 against those ending in the trit 2, computes hundreds of zeros of the Riemann zeta function and of the L-function behind base 3 from scratch, and rebuilds the prime staircases from those zeros. Digit statistics are compared with matched control groups – including a false positive that the lab catches and explains.

The findings: the trits of a prime carry no information about primality beyond 2 and 3, and base 2 and base 3 see exactly the same. The primes ending in trit 2 lead those ending in trit 1 up to 608,981,813,029 – for a reason that is fully explained. Consecutive primes avoid repeating their last trit. Ternary-shaped numbers such as 2·3ⁿ + 1 can be proven prime with a single exponentiation. And the Riemann hypothesis itself is not a question about digits.

Also inside: an inspector for any number or expression, a prover with Pocklington and Morrison certificates, pattern views, and five open problems – Artin's conjecture for base 3, primes with missing trits, Mirimanoff primes, ternary repunits and Erdős's ternary conjecture. Everything is computed locally; nothing is downloaded or sent.