A public evidence package for 11 certified least-n results.
This is a computational result about the Riesel base-71 conjecture. For each of 11 previously unproven k-values on the CRUS "Riesel base 71 remain" list, the least n such that k·71^n − 1 is prime was found and certified. Every smaller n is provably composite, and every prime is proven three independent ways (GMP Miller–Rabin, sympy BPSW, and a Brillhart–Lehmer–Selfridge Lucas N+1 proof).
Read the full report · Verify every certificate · Download the certificates · Inspect the raw results
Download the two-page infographic PDF · Open the social header image
| k | least n | digits | Lucas D |
|---|---|---|---|
| 1000004 | 1266 | 2350 | 5 |
| 1000034 | 1176 | 2184 | −19 |
| 1000174 | 2101 | 3896 | −19 |
| 1000222 | 1679 | 3115 | 53 |
| 1000834 | 3571 | 6617 | 61 |
| 1000892 | 2678 | 4964 | 21 |
| 1001020 | 2963 | 5492 | 21 |
| 1001072 | 1014 | 1884 | 65 |
| 1001248 | 1421 | 2637 | 5 |
| 1001332 | 2731 | 5062 | 37 |
| 1001464 | 1405 | 2608 | 5 |
verify.py recomputes each integer, proves that the listed qs values completely factor N+1, checks the supplied Lucas witness, and cross-checks sympy.isprime(N).
python3 -m venv .venv
source .venv/bin/activate
python -m pip install -r requirements.txt
python verify.py data/riesel-71-certificates.jsonlThe verification record contains the exact output from a clean run. The original settlement and certification engines are preserved as riesel-71-batch.py and riesel-71-certify.py.
The base-71 conjecture itself is NOT solved — 19,068,114 k's remain open.
The source k-list is Gary Barnes's CRUS remain-riesel-base71.zip, file dated Nov 2 2025, from the CRUS Riesel conjectures page. Status is stated only for the Oct 23 2025 base-page window and the Jul 22 2026 reservations snapshot. CRUS coordination is via Mersenneforum thread 6722.
Earlier related Beal and Sun computational work is preserved separately in the beal-sun index.
Data and text are released under CC0 1.0. Code is released under the MIT License. See LICENSE.md.