Distributed Prime Discovery
Hunt special-form primes across CPU clusters. 12 algorithms. Deterministic proofs. Open source.
12 Prime Forms
From classical factorial primes to exotic generalized Fermats — Darkreach searches them all with form-specific sieves, tests, and proofs.
Factorial
Pocklington / MorrisonPrimes adjacent to factorial numbers. GMP factorial computation with modular sieve elimination.
Primorial
Pocklington / MorrisonPrimes adjacent to the product of all primes up to p. Similar structure to factorials but denser.
Proth / Riesel
Proth test / LLRThe workhorse form. Covers Proth numbers (k·2ⁿ+1) and Riesel numbers (k·2ⁿ−1) with BSGS sieve.
Cullen / Woodall
Proth test / LLRCullen numbers (n·2ⁿ+1) and Woodall numbers (n·2ⁿ−1). Special case of k·bⁿ±1 with k=n.
Generalized Fermat
Pépin / ProthGeneralization of Fermat numbers F_n = 2^(2ⁿ)+1 to arbitrary bases. Pépin-style testing.
Wagstaff
Vrba-Reix PRPWagstaff numbers for prime p. No deterministic proof exists — results are probable primes (PRP).
Carol / Kynea
LLR testCarol primes (2ⁿ−1)²−2 and Kynea primes (2ⁿ+1)²−2. Sparse but fast to test.
Twin Primes
Proth + LLRPairs of primes separated by 2. Quad sieve eliminates candidates, then Proth+LLR intersection.
Sophie Germain
Proth + LLRPrime p where 2p+1 is also prime. Foundation for safe primes used in cryptography.
Palindromic
Miller-RabinPrimes that read the same forwards and backwards in a given base. Deep sieve with batch generation.
Near-Repdigit
BLS proofPalindromic primes where all digits are the same except one. BLS N+1 proofs available.
Repunit
PFGW PRPNumbers consisting entirely of 1s in base b. Extremely rare primes — only 11 known decimal repunit primes.
How It Works
Every candidate passes through a three-stage pipeline optimized for each prime form.
Sieve
Eliminate composites with form-specific sieves — wheel factorization, BSGS, and Pollard P−1 filtering before any heavy computation.
Test
Run Miller-Rabin pre-screening, then form-specific primality tests — Proth, LLR, Pépin — accelerated by PFGW and GWNUM FFT.
Prove
Generate deterministic primality certificates — Pocklington, Morrison, BLS — with independently verifiable witness data.
Recent Discoveries
A sample of primes found by the Darkreach network.
| Form | Expression | Digits | Proof | Date |
|---|---|---|---|---|
| Factorial | 147855! + 1 | 636,919 | Pocklington | 2026-02-14 |
| Proth | 87 · 2^1,290,473 + 1 | 388,342 | Proth test | 2026-02-12 |
| Twin | 3 · 2^850,121 ± 1 | 255,891 | Proth + LLR | 2026-02-10 |
| Palindromic | 1 [0]₃₇₅₁₂ 1 | 37,514 | BPSW + MR₁₀ | 2026-02-08 |
| Primorial | 1648079# + 1 | 715,021 | Morrison | 2026-02-05 |
| Gen. Fermat | 142^65536 + 1 | 141,116 | Pépin | 2026-01-29 |
| Sophie Germain | 21 · 2^641,008 − 1 | 192,971 | LLR | 2026-01-25 |
| Cullen | 6,679,881 · 2^6,679,881 + 1 | 2,010,852 | Proth test | 2026-01-18 |
| Repunit | R(10, 86,453) | 86,453 | PFGW PRP | 2026-01-11 |
| Wagstaff | (2^1,284,057 + 1) / 3 | 386,614 | Vrba-Reix PRP | 2026-01-04 |
Why Darkreach
How Darkreach compares to existing distributed prime search platforms.
| Feature | Darkreach | GIMPS | PrimeGrid |
|---|---|---|---|
| Prime forms supported | 12 | 1 (Mersenne) | ~6 |
| Deterministic proofs | Yes (Pocklington, Morrison, BLS) | Yes (Lucas-Lehmer) | Partial |
| Modern dashboard | Yes (real-time, charts, search mgmt) | Basic web | BOINC client |
| Open source | Yes (MIT) | No | Partially |
| Self-hostable | Yes (single binary + Postgres) | No | No |
| Proof certificates | JSONB witnesses, independently verifiable | Internal | None |
Get Started
Install from source and start hunting primes in minutes.
Build from source
# Requires Rust and GMP
git clone https://github.com/darkreach/darkreach.git
cd darkreach
cargo build --releaseRun a search
# Search for factorial primes from 1000! to 5000!
./target/release/darkreach factorial --start 1000 --end 5000
# Search Proth primes k·2^n+1
./target/release/darkreach kbn --k 3 --base 2 --min-n 100000 --max-n 200000