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A.P. · 置顶
发布时间：2026-09-18 08:05:41 UTC
最后编辑时间：2026-11-07 10:13:21 UTC
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 |
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## 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 |
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