Research Initiative
Prime Number Discovery
Searching 12 special forms of prime numbers with deterministic proofs. Every candidate sieved, tested, and proven across a distributed compute network.
Why primes matter
Prime numbers are the atoms of mathematics. Their study drives breakthroughs in security, computation, and pure mathematics.
Cryptography
Large primes underpin RSA, Diffie-Hellman, and elliptic curve cryptography. Discovering new primes pushes the boundary of what's computationally feasible.
Unsolved Conjectures
Twin prime conjecture, Goldbach's conjecture, and the distribution of primes remain open. Computational evidence drives mathematical progress.
Mathematical Beauty
Special-form primes — factorial, palindromic, Sophie Germain — reveal deep structure in number theory that pure theory can't yet explain.
Verification Challenge
Proving a number prime requires deterministic certificates. Our 3-tier pipeline guarantees every discovery is independently verifiable.
Prime Forms
12 specialized searches
Each form has a dedicated sieve, primality test, and proof strategy.
Factorial
Pocklington / MorrisonPrimes adjacent to factorial numbers. GMP factorial computation with modular sieve elimination.
Learn more →Primorial
Pocklington / MorrisonPrimes adjacent to the product of all primes up to p. Similar structure to factorials but denser.
Learn more →Proth / Riesel
Proth test / LLRThe workhorse form. Covers Proth numbers (k·2ⁿ+1) and Riesel numbers (k·2ⁿ−1) with BSGS sieve.
Learn more →Cullen / Woodall
Proth test / LLRCullen numbers (n·2ⁿ+1) and Woodall numbers (n·2ⁿ−1). Special case of k·bⁿ±1 with k=n.
Learn more →Generalized Fermat
Pépin / ProthGeneralization of Fermat numbers F_n = 2^(2ⁿ)+1 to arbitrary bases. Pépin-style testing.
Learn more →Wagstaff
Vrba-Reix PRPWagstaff numbers for prime p. No deterministic proof exists — results are probable primes (PRP).
Learn more →Carol / Kynea
LLR testCarol primes (2ⁿ−1)²−2 and Kynea primes (2ⁿ+1)²−2. Sparse but fast to test.
Learn more →Twin Primes
Proth + LLRPairs of primes separated by 2. Quad sieve eliminates candidates, then Proth+LLR intersection.
Learn more →Sophie Germain
Proth + LLRPrime p where 2p+1 is also prime. Foundation for safe primes used in cryptography.
Learn more →Palindromic
Miller-RabinPrimes that read the same forwards and backwards in a given base. Deep sieve with batch generation.
Learn more →Near-Repdigit
BLS proofPalindromic primes where all digits are the same except one. BLS N+1 proofs available.
Learn more →Repunit
PFGW PRPNumbers consisting entirely of 1s in base b. Extremely rare primes — only 11 known decimal repunit primes.
Learn more →How it works
Discovery Pipeline
Every candidate passes through four stages. Only proven primes survive.
Sieve
ELIMINATED
Wheel factorization, BSGS, and Pollard P-1 filtering remove composites before testing.
Test
MR ROUNDS
Proth, LLR, Pépin, and Frobenius tests accelerated by PFGW for large candidates.
Prove
DETERMINISTIC
Pocklington, Morrison, and BLS certificates with full witness data. Verifiable.
Coordinate
BLOCK CLAIM
Operator nodes claim work blocks via PostgreSQL. Results verified through trust-based quorum with adaptive replication.
Sieve
ELIMINATED
Wheel factorization, BSGS, and Pollard P-1 filtering remove composites before testing.
Test
MR ROUNDS
Proth, LLR, Pépin, and Frobenius tests accelerated by PFGW for large candidates.
Prove
DETERMINISTIC
Pocklington, Morrison, and BLS certificates with full witness data. Verifiable.
Coordinate
BLOCK CLAIM
Operator nodes claim work blocks via PostgreSQL. Results verified through trust-based quorum with adaptive replication.
Sieve
STEP 1
Wheel factorization, BSGS, and Pollard P-1 filtering remove composites before testing.
Test
STEP 2
Proth, LLR, Pépin, and Frobenius tests accelerated by PFGW for large candidates.
Prove
STEP 3
Pocklington, Morrison, and BLS certificates with full witness data. Verifiable.
Coordinate
STEP 4
Operator nodes claim work blocks via PostgreSQL. Results verified through trust-based quorum with adaptive replication.
Discoveries
Latest primes found by the network, updated in real time.
Comparison
Why darkreach
The first modern, AI-driven prime search platform.
| Feature | darkreach | GIMPS | PrimeGrid |
|---|---|---|---|
| Multiple prime forms | 12 forms | Mersenne only | ~6 forms |
| AI strategy optimization | Autonomous form selection | ||
| Operator system with trust levels | Registered operators with API keys | ||
| Node registration & monitoring | My Nodes dashboard | BOINC client | |
| Role-based team access | Admin/operator roles | ||
| Operator leaderboard | Credit-based rankings | BOINC credits | |
| Open source | MIT license | ||
| Self-hostable | Single binary | ||
| Real-time dashboard | WebSocket + charts | Basic web UI | BOINC client |
| Proof certificates | Verifiable JSONB | Internal only |
Ready to contribute?
Join the network as an operator and help discover the next prime, or explore the complete documentation for all 12 search forms.