| GIMPS | TF | 2 | trial factoring | screen for not-prime, assigned as factoring |
| GIMPS | PM1-S | 3 | factor P-1 small | screen for not-prime, assigned as factoring |
| GIMPS | PM1-L | 4 | factor P-1 large | screen for not-prime, assigned as P-factoring |
| GIMPS | ECM | 5 | factor ECM small | screen for not-prime, assigned as ECM |
| GIMPS | PP1 | 6 | factor P+1 | screen for not-prime, assigned as P+1 factoring |
| GIMPS | TF-LMH | 90 | trial factoring LMH | screen for not-prime, factoring to low limits |
| GIMPS | PM1-R | 95 | factor P-1 redo | screen for not-prime, reassigned as P-factoring |
| GIMPS | LL | 100 | LL first test | primality test, assigned as first LL test |
| GIMPS | D | 101 | LL double-check | primality test, assigned as LL verification |
| GIMPS | PRP | 150 | PRP test | probable prime test, assigned as PRP test |
| GIMPS | PRP-D | 151 | PRP double-check | probable prime test, assigned as PRP verification |
| GIMPS | PRP-CF | 160 | PRP cofactor test | probable prime test, assigned as PRP cofactor test |
| GIMPS | PRP-CF-D | 161 | PRP cofactor test double-check | probable prime test, assigned as PRP cofactor verification |
| GIMPS | CERT | 200 | PRP proof certification | proof verification, assigned to reliable computers |
