New Mersenne Prime discovered (probably)

Original Article ↗ Hacker News Discussion ↗

Overall tone

  • Strong enthusiasm and nostalgia from people who used to or still run GIMPS/Prime95.
  • Mix of “this is cool for its own sake” with questions about real-world utility and cost.
  • Plenty of humor and pop‑culture references alongside serious number-theory discussion.

Why the prime is initially secret

  • Some suggest it’s to protect eligibility for EFF large-prime awards; another commenter who ran those awards says the new prime is unlikely to be big enough and thinks the embargo is mainly for scientific integrity until verification.
  • Clarification that the EFF prize is awarded for a proved prime; whoever produces the deterministic proof gets the credit, regardless of who first generated the candidate, hence the incentive to embargo.
  • It’s noted that, in principle, someone could try to infer the candidate from GIMPS status data, but it’s nontrivial.

What Mersenne primes are and how they’re tested

  • Mersenne primes are primes of the form 2ⁿ − 1; n must be prime, but that alone doesn’t guarantee primality.
  • Many examples of composite 2ⁿ − 1 are given.
  • GIMPS uses specialized tests: historically Lucas–Lehmer, now first-time probabilistic (Fermat PRP) tests plus strong certificates, with later deterministic proofs.
  • One comment incorrectly claims infinite perfect numbers (and thus infinite Mersenne primes); others explain this is not known and that Euclid’s proof of infinitely many primes does not extend to Mersenne primes.

Organization, verification, and credit

  • Exponents are assigned and later re-assigned for independent checks; primes aren’t marked “done” until results are reported.
  • Questions arise about who is recognized as “discoverer” among those doing different tasks (PRP tests, factoring, certification). Consensus leans toward crediting the PRP/LL tester, though incentives are debated.

Purpose and usefulness

  • Motivations: exploration, learning about primes, improving algorithms, and sheer challenge (“because it’s there”).
  • Several clarify that record primes are not directly useful for cryptography, which uses much smaller primes.
  • Some compare the project to space exploration with tech spinoffs (optimized arithmetic algorithms).

Scale, cost, and alternative compute uses

  • GIMPS’s reported throughput: ~127 PFlop/s, comparable to a top-10 supercomputer.
  • Rough back-of-envelope estimate: matching that on cloud GPUs might cost on the order of millions of dollars per year, not tens of thousands.
  • Discussion of prime-based cryptocurrencies (Primecoin, Gapcoin, Riecoin, Nexus) and concerns that “interesting” PoW functions invite secret optimizations.
  • Suggestions that more distributed computing should target obviously useful work (protein folding, climate, superoptimizing code).

Implementation details & tooling

  • People use Prime95 and y-cruncher for hardware stress testing; some want an Apple Silicon Prime95 build.
  • GPU-based Mersenne testing exists (e.g., gpuowl).
  • Laptops often run too hot for sustained GIMPS work; users experiment with throttling.

Humor and side threads

  • Jokes about Bruce Schneier, Chuck Norris, aliens using hidden Mersenne primes for first contact, and missed Bitcoin-mining opportunities.
  • Various anecdotes about near-miss riches (lottery systems, early Bitcoin faucets) parallel “almost discovering” primes.