The Prime number tester

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An integer greater than one is prime if its only positive divisors are itself and one (otherwise it is composite). For example: 15 is composite because it has the two prime divisors 3 and 5.

Prime numbers:

```      2      3      5      7     11     13     17     19     23     29
31     37     41     43     47     53     59     61     67     71
73     79     83     89     97    101    103    107    109    113
127    131    137    139    149    151    157    163    167    173
179    181    191    193    197    199    211    223    227    229
233    239    241    251    257    263    269    271    277    281
283    293    307    311    313    317    331    337    347    349
353    359    367    373    379    383    389    397    401    409
419    421    431    433    439    443    449    457    461    463
467    479    487    491    499    503    509    521    523    541
547    557    563    569    571    577    587    593    599    601
607    613    617    619    631    641    643    647    653    659
661    673    677    683    691    701    709    719    727    733
739    743    751    757    761    769    773    787    797    809
811    821    823    827    829    839    853    857    859    863
877    881    883    887    907    911    919    929    937    941
947    953    967    971    977    983    991    997   1009   1013
1019   1021   1031   1033   1039   1049   1051   1061   1063   1069
1087   1091   1093   1097   1103   1109   1117   1123   1129   1151
1153   1163   1171   1181   1187   1193   1201   1213   1217   1223
1229   1231   1237   1249   1259   1277   1279   1283   1289   1291
1297   1301   1303   1307   1319   1321   1327   1361   1367   1373
1381   1399   1409   1423   1427   1429   1433   1439   1447   1451
1453   1459   1471   1481   1483   1487   1489   1493   1499   1511
1523   1531   1543   1549   1553   1559   1567   1571   1579   1583
1597   1601   1607   1609   1613   1619   1621   1627   1637   1657
1663   1667   1669   1693   1697   1699   1709   1721   1723   1733
1741   1747   1753   1759   1777   1783   1787   1789   1801   1811
1823   1831   1847   1861   1867   1871   1873   1877   1879   1889
1901   1907   1913   1931   1933   1949   1951   1973   1979   1987
1993   1997   1999   2003   2011   2017   2027   2029   2039   2053
2063   2069   2081   2083   2087   2089   2099   2111   2113   2129
2131   2137   2141   2143   2153   2161   2179   2203   2207   2213```

If you square any prime number bigger then 3, then subtract 1, the answer always divides by 24.

Related

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