Bellpair · interactive lab
Inside a Bellpair receipt.
Choose a base. Inspect the two contributions.
Follow the receipt through verification.
Waiting for work
Waiting for work
The table assigns matching weights before the search.
The work is to find qualifying primes with those endings.
- Attempts · recorded
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- Search time
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- Prime tests
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- Workers
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The verification checks
- The issued challenge, number base, message hash, difficulty, expiry and assigned roles.
- Both SHA-256 hashes, recomputed from the nonces and canonical message.
- The derived prime candidates, primality, endings in the chosen base and table balance.
- At redemption: a known, unexpired and unused challenge.
The collision periodic table
Different endings.
Exact counterparts.
Every eligible ending has a reflected partner. The raw fingerprints add to −1. Centering and doubling gives opposite integers.
Base 16 has 64 reflected pairs. The highlighted entries are the roles assigned to this challenge.
Read the protocolThe challenge’s selected pair is highlighted.
0F → +29 / F1 → −29
Ten bases · 1,920 native trials
Base choice changes the work.
More eligible endings spread the prime search across more roles. At the same hash threshold, a prescribed pair usually takes more work to find.
| Base | Pairs | Mean attempts | Mean search |
|---|---|---|---|
| 2 | 1 | 1,488 | 2.1 ms |
| 3 | 3 | 4,223 | 5.8 ms |
| 4 | 4 | 6,237 | 8.5 ms |
| 5 | 10 | 15,967 | 19.2 ms |
| 6 | 6 | 9,590 | 11.3 ms |
| 8 | 16 | 24,311 | 28.0 ms |
| 10 | 20 | 29,585 | 34.4 ms |
| 12 | 24 | 30,892 | 35.7 ms |
| 16 | 64 | 102,956 | 118.0 ms |
| 30 | 120 | 167,341 | 191.1 ms |
96 receipts per base per policy · one worker · C/GMP · Intel Core i9-13900H. These experiments use a separate audit hash domain and adjustable thresholds. They establish a cost tradeoff; they do not establish a fastest base or a security advantage. All trials and metadata
Base 10 · retained measurements
The cost of each added constraint.
The same hash difficulty, with one filter added at a time. These are measured costs, not a matched-cost security comparison.
| Required work | Mean attempts | Mean time / pair |
|---|---|---|
| Hash difficulty only | 651 | 1.155 ms |
| Hash + selected endings | 59,987 | 78.630 ms |
| Hash + endings + two primes | 956,518 | 1269.027 ms |
12 pairs per method · 6, 8 and 10 hash bits · one worker · mean repeated arithmetic verification 0.031 ms. Timings exclude process and server startup. Complete data
The reference implementation uses C, GMP and OpenMP. Inspect the recorded walkthrough here, or download the MIT-licensed code to run your own searches, check receipts and change the implementation locally.