## GFPS-16
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :----: | :---: | :---: | :---: | :---: | :---: |
| (1814570322493370-1814570322693368) ^ 65536 + 1 | 999999 | 100000 | 32048, sieved up to 1e17 | 1 | 1814570322533286^65536+1 |

## GFPS-Misc
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :----: | :---: | :---: | :---: | :---: | :---: |
| 867 bases from GFN16 to GFN17 | 1140925~1151476 | 867 | 288, sieved up to 1e17 | 0 | - |

## GPRPS
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :----: | :---: | :---: | :---: | :---: | :---: |
|(2-100000) * 1337 ^ 0x13337 ± 1 | 245862~245866 | 100000 | 3940, sieved up to 5e14 | 0 | - |

## KBBPS
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :---: | :---: | :---: | :---: | :---: | :---: |
| (2-100000) * 0x1337 ^ 0x1337 ± 1 | 18161 ~ 18166 | 100000 | 3652, sieved up to 2e13 | 3 | 7518\*0x1337^0x1337+1, 37792\*0x1337^0x1337-1, 71442\*0x1337^0x1337+1 |
| (2-100000) * 13337 ^ 13337 ± 1 | 55016 ~ 55021 | 100000 | 3527, sieved up to 5e13 | 1 | 54940\*13337^13337-1 |
| (2-100000) * 31337 ^ 31337 ± 1 | 140894 ~ 140898 | 100000 | 3441, sieved up to 1e14 | 0 | - |
| (2-100000) * 32500 ^ 32500 ± 1 | 146637 ~ 146642 | 200000 | 9061, sieved up to 2e14 | 3 | 11127\*32500^32500+1, 23424\*32500^32500+1, 65373\*32500^32500+1 |

## GNCWPS
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :---: | :---: | :---: | :---: | :---: | :---: |
| (20002-100000) * 7 ^ (20003-100001) - 1 | 16909 ~ 84516 | 40000 | 1856, sieved up to 1e12 | 1 | 66980\*7^66981-1 |
| (20002-100000) * 7 ^ (20001-99999) - 1 | 16908 ~ 84515 | 40000 | 1951, sieved up to 1e12 | 2 | 49784\*7^49783-1, 53106\*7^53105-1 |
| (20002-100000) * 7 ^ (20003-100001) + 1 | 16909 ~ 84516 | 40000 | 1708, sieved up to 1e12 | 1 | 37170\*7^37171+1 |
| (20002-100000) * 7 ^ (20001-99999) + 1 | 16908 ~ 84515 | 40000 | 1795, sieved up to 6e11 | 1 | 47254\*7^47253+1 |
| (10002-100000) * 77 ^ (10003-100001) - 1 | 18875 ~ 188656 | 45000 | 2334, sieved up to 1e12 | 2 | 20020\*77^20021-1, 82846\*77^82847-1 |
| (10002-100000) * 77 ^ (10001-99999) - 1 | 18871~188653 | 45000 | 2326, sieved up to 1e12 | 0 | - |
| (10002-100000) * 77 ^ (10003-100001) + 1 | 18875~188656 | 45000 | 2385, sieved up to 1e12 | 1 | 11406\*77^11407+1 |
| (10002-100000) * 77 ^ (10001-99999) + 1 | 18871~188653 | 45000 | 2369, sieved up to 1e12 | 0 | - |


## GHCWPS
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 7 ^ (50002-500000) * (50002-500000) ^ 7 ± 1 | 42290~422589 | 450000 | 16826, sieved up to 2e10+5e10 | 1 | 7^119982*119982^7-1 |


## GFPPS-MUL
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :---: | :---: | :---: | :---: | :---: | :---: |
| (2-25206) * 25206! ± 1 | 100001 ~ 100005 | 50410 | 16226, sieved up to 5e13 | 4 | 5037\*25206!-1, 17165\*25206!-1, 17380\*25206!+1, 20698\*25206!-1 |


## GFPPS-DIV
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :---: | :---: | :---: | :---: | :---: | :---: |
| 26951! / (2-26950) ± 1 | 107702 ~ 107706 | 53898 | 17822, sieved up to 3e13 | 5 | 26951!/1327+1, 26951!/1427+1, 26951!/3309-1, 26951!/17834+1, 26951!/24341-1 |


## RGFPS
| Format | Decimal Digits | Initial Cands | Sieved Cands | Count of Primes | Primes |
| :----: | :---: | :---: | :---: | :---: | :---: |
| P0 = 1, P[k+1] = (2\*m\*P[k])^2+1, min(m) in [1,2000000] for P[19] | 608062 ~ 608075 | 2000000 | 85607, sieved up to 5e15 | 1 | (1721592*P18)^2+1 |