Definition
The GM / GQ conjugate pair
For every odd prime exponent p, GMNet tracks both conjugate factors of the Gaussian Mersenne norm:
GQp = 2p + (2/p)2(p+1)/2 + 1
Work and results carry an explicit target_family value: GM, GQ, or BOTH. PrMers reuses the exact GPU lift to 2^(4p)-1 and classifies every reported divisor on the server.
Algorithms
Five complementary methods
GMTF sieves factors in a bit range. A BOTH assignment shares the exponent work and reports every GM and GQ divisor found.
Fast search for factors whose q-1 is smooth. Bounds increase progressively.
Searches factors using multiple Montgomery curves after the P-1 tiers.
Screens candidates as probable primes and requires an independent matching run.
Runs the deterministic Proth primality test for positive candidates.
Integrity
Verification workflow
- Every submitted GM or GQ factor is checked by exact modular division on the server.
- GPU TF coverage records the family and tested bit interval, including no-factor completion.
- No-factor results advance only the assigned algorithm tier.
- PRP and exact tests are coordinated across distinct contributors.
- Known historical primes are stored separately from GMNet discoveries.
Work profiles
Screening and mixed campaigns
Uses a larger B1 with B2 equal to B1. Stage 2 is disabled, making it suitable for fast screening across large ranges.
Runs P-1 Stage 1 and Stage 2 first, then continues with ECM only when P-1 found no factor, and stops after factoring without running Proth.
GMRelay can keep either profile filled automatically while PrMers writes and GMRelay submits the normal result JSON files.
PrMers integration
Native worktodo formats
GMTF=p,from_bits,to_bits[,sieve_prime[,chunk_candidates[,target_family]]]
GMPMINUS1=p,B1,B2[,base[,sieve_limit[,chunk_bits]]]
GMECM=p,B1,B2,curves[,sigma[,sieve_limit[,chunk_bits]]]
GMCHAIN=p,pm1_B1,pm1_B2,ecm_B1,ecm_B2,curves[,sieve_limit[,chunk_bits]]
GMPRP=p[,sieve_limit]
GMPROTH=p[,sieve_limit]External sources