Prime Resonance Ladder

Selected primes as living states. Generate the next state by scanning candidate primes and choosing the one that best extends the ladder’s resonance.

Sequence

Prime ladder input (comma, space, or newline separated)

BigInt + probable-prime search

Terms

Last prime

—

Partial sum

—

Last log step

—

Selection rule

a_n+1 = argmax_{p ∈ P} R(p | a₁, …, a_n)

This page approximates resonance with weighted contributions from scale coherence, closeness to a predicted target, digit affinity, historical shape, and relation to the accumulated field.

Resonance controls

Scale weight 1.20 Target weight 1.60 Digit weight 0.80 History weight 0.75 Series weight 0.55 Candidate count Search half-window Prediction mode

Prime ladder and partial sums

Blue line: log-scaled prime ladder. Green line: log-scaled partial sums. The active term is highlighted.

Selected state

#	Prime state	Partial sum	Gap	Log step

Candidate primes ranked by resonance

Rank	Candidate prime	Total score	Scale	Target	Digit	History	Series

Notes

This tool treats your sequence as selected primes, not a forced recurrence. The next state is chosen from nearby candidate primes and ranked by a resonance functional.

Because the ladder can contain very large primes, the primality engine uses probable-prime testing with BigInt modular arithmetic. For artistic exploration and ladder-building this is usually sufficient.

Try changing the seed sequence, then press Select next prime repeatedly. You can also play the ladder as tones; larger primes map to higher frequencies on a compressed logarithmic scale.