Near-Wilson Primes
- A prime p satisfying the congruence (p − 1)! ≡ − 1 + Bp (mod p2) with small |B| can be called a near-Wilson prime. Near-Wilson primes with B = 0 represent Wilson primes. The following table lists all such primes with |B| ≤ 100 from 106 up to 4×1011:
| p | B |
|---|---|
| 1282279 | +20 |
| 1306817 | −30 |
| 1308491 | −55 |
| 1433813 | −32 |
| 1638347 | −45 |
| 1640147 | −88 |
| 1647931 | +14 |
| 1666403 | +99 |
| 1750901 | +34 |
| 1851953 | −50 |
| 2031053 | −18 |
| 2278343 | +21 |
| 2313083 | +15 |
| 2695933 | −73 |
| 3640753 | +69 |
| 3677071 | −32 |
| 3764437 | −99 |
| 3958621 | +75 |
| 5062469 | +39 |
| 5063803 | +40 |
| 6331519 | +91 |
| 6706067 | +45 |
| 7392257 | +40 |
| 8315831 | +3 |
| 8871167 | −85 |
| 9278443 | −75 |
| 9615329 | +27 |
| 9756727 | +23 |
| 10746881 | −7 |
| 11465149 | −62 |
| 11512541 | −26 |
| 11892977 | −7 |
| 12632117 | −27 |
| 12893203 | −53 |
| 14296621 | +2 |
| 16711069 | +95 |
| 16738091 | +58 |
| 17879887 | +63 |
| 19344553 | −93 |
| 19365641 | +75 |
| 20951477 | +25 |
| 20972977 | +58 |
| 21561013 | −90 |
| 23818681 | +23 |
| 27783521 | −51 |
| 27812887 | +21 |
| 29085907 | +9 |
| 29327513 | +13 |
| 30959321 | +24 |
| 33187157 | +60 |
| 33968041 | +12 |
| 39198017 | −7 |
| 45920923 | −63 |
| 51802061 | +4 |
| 53188379 | −54 |
| 56151923 | −1 |
| 57526411 | −66 |
| 64197799 | +13 |
| 72818227 | −27 |
| 87467099 | −2 |
| 91926437 | −32 |
| 92191909 | +94 |
| 93445061 | −30 |
| 93559087 | −3 |
| 94510219 | −69 |
| 101710369 | −70 |
| 111310567 | +22 |
| 117385529 | −43 |
| 176779259 | +56 |
| 212911781 | −92 |
| 216331463 | −36 |
| 253512533 | +25 |
| 282361201 | +24 |
| 327357841 | −62 |
| 411237857 | −84 |
| 479163953 | −50 |
| 757362197 | −28 |
| 824846833 | +60 |
| 866006431 | −81 |
| 1227886151 | −51 |
| 1527857939 | −19 |
| 1636804231 | +64 |
| 1686290297 | +18 |
| 1767839071 | +8 |
| 1913042311 | −65 |
| 1987272877 | +5 |
| 2100839597 | −34 |
| 2312420701 | −78 |
| 2476913683 | +94 |
| 3542985241 | −74 |
| 4036677373 | −5 |
| 4271431471 | +83 |
| 4296847931 | +41 |
| 5087988391 | +51 |
| 5127702389 | +50 |
| 7973760941 | +76 |
| 9965682053 | −18 |
| 10242692519 | −97 |
| 11355061259 | −45 |
| 11774118061 | −1 |
| 12896325149 | +86 |
| 13286279999 | +52 |
| 20042556601 | +27 |
| 21950810731 | +93 |
| 23607097193 | +97 |
| 24664241321 | +46 |
| 28737804211 | −58 |
| 35525054743 | +26 |
| 41659815553 | +55 |
| 42647052491 | +10 |
| 44034466379 | +39 |
| 60373446719 | −48 |
| 64643245189 | −21 |
| 66966581777 | +91 |
| 67133912011 | +9 |
| 80248324571 | +46 |
| 80908082573 | −20 |
| 100660783343 | +87 |
| 112825721339 | +70 |
| 231939720421 | +41 |
| 258818504023 | +4 |
| 260584487287 | −52 |
| 265784418461 | −78 |
| 298114694431 | +82 |
Read more about this topic: Wilson Prime