Try Any Number

Type a number. The axiom searches for its simplest expression in five primes {2, 3, 5, 7, 11}. Built-in null model. Honest errors.

alpha (137) 5/3 proton Higgs BCS Kleiber CMB 42

or choose a known constant below

The Pattern

35 constants above. Mean error: --. Exact matches: --. This is not curve-fitting — these are simple ratios of five primes.

Individual approximate matches may not be significant alone — the signal is the collective pattern across dozens of constants. Named expressions (SOUL, HYDOR, GATE) use axiom-derived values beyond the five primes.

Verify any expression: open the .ax REPL and type it. Or see all 70+ constants with full derivations.

How this works

The search generates all numbers of the form 2^a · 3^b · 5^c · 7^d · 11^e with small exponents, plus extensions with pi and sqrt.

Null model

For each match, we count actual smooth rationals near the target in our database and compute how likely a random number would match at equal or better precision.

green: fewer than 1% of randoms match (strong)
yellow: 1-5% or named expression (suggestive / N/A)
red: over 5% (not individually significant)

Many approximate matches (0.1-1% error) are not individually significant — there are many smooth rationals. The signal is the collective pattern: 18 exact matches + a dozen sub-percent matches across 35 constants is astronomically unlikely.

Constants using named axiom values (SOUL=67, HYDOR=105, GATE=13) go beyond the five primes. These can't be tested by the single-smooth null model.

Complexity

Sum of absolute exponents in the prime factorization. Lower = simpler. A match is more impressive when complexity is low AND error is small.

What this proves

No single match proves anything. The pattern across dozens of constants — with exact hits, sub-ppm precision, and structural meaning — is what demands explanation.

The axiom derives from 0/0 = Z/970200Z. Details: the full story.