492:
278:
198:
All such prime decades have centers of form 210n + 15, 210n + 105, and 210n + 195 since the centers must be -1, O, or +1 modulo 7. The +15 form may also give rise to a (high) prime quintuplet; the +195 form can also give rise to a (low) quintuplet; while the +105 form can yield both types of quints
807:
It is not known if there are infinitely many prime quintuplets. Once again, proving the twin prime conjecture might not necessarily prove that there are also infinitely many prime quintuplets. Also, proving that there are infinitely many prime quadruplets might not necessarily prove that there are
487:{\displaystyle B_{4}=\left({\frac {1}{5}}+{\frac {1}{7}}+{\frac {1}{11}}+{\frac {1}{13}}\right)+\left({\frac {1}{11}}+{\frac {1}{13}}+{\frac {1}{17}}+{\frac {1}{19}}\right)+\left({\frac {1}{101}}+{\frac {1}{103}}+{\frac {1}{107}}+{\frac {1}{109}}\right)+\cdots }
1065:
1082:
might not necessarily prove that there are also infinitely many prime sextuplets. Also, proving that there are infinitely many prime quintuplets might not necessarily prove that there are infinitely many prime sextuplets.
199:
and possibly prime sextuplets. It is no accident that each prime in a prime decade is displaced from its center by a power of 2, actually 2 or 4, since all centers are odd and divisible by both 3 and 5.
221:, but it is consistent with current knowledge that there may be infinitely many pairs of twin primes and only finitely many prime quadruplets. The number of prime quadruplets with
945:
191:. (This structure is necessary to ensure that none of the four primes are divisible by 2, 3 or 5). A prime quadruplet of this form is also called a
214:. These "quad" primes 11 or above also form the core of prime quintuplets and prime sextuplets by adding or subtracting 8 from their respective centers.
935:
A prime sextuplet contains two close pairs of twin primes, a prime quadruplet, four overlapping prime triplets, and two overlapping prime quintuplets.
2085:
1317:
1688:
1136:
Prime quadruplets, quintuplets, and sextuplets are examples of prime constellations, and prime constellations are in turn examples of prime
2591:
889:
792:
734:
606:
243:
157:
1770:
1693:
1607:
217:
It is not known if there are infinitely many prime quadruplets. A proof that there are infinitely many would imply the
1310:
804:
A prime quintuplet contains two close pairs of twin primes, a prime quadruplet, and three overlapping prime triplets.
2586:
1087:
812:
618:
1944:
2025:
1250:
1303:
2147:
1805:
1718:
2172:
236:
1, 3, 7, 27, 128, 733, 3869, 23620, 152141, 1028789, 7188960, 51672312, 381226246, 2873279651 (sequence
2080:
1638:
2109:
691:
which is the closest admissible constellation of five primes. The first few prime quintuplets with
56:
1713:
932:
follows from defining a prime sextuplet as the closest admissible constellation of six primes.
2230:
1359:
2567:
2157:
1810:
1079:
550:
Excluding the first prime quadruplet, the shortest possible distance between two quadruplets
250:
As of
February 2019 the largest known prime quadruplet has 10132 digits. It starts with
218:
55:
This represents the closest possible grouping of four primes larger than 3, and is the only
2137:
8:
2132:
1790:
1795:
2240:
2177:
2167:
2152:
1785:
1643:
1564:
1283:
1265:
1078:
It is not known if there are infinitely many prime sextuplets. Once again, proving the
261:
1251:"On The Asymptotic Density Of Prime k-tuples and a Conjecture of Hardy and Littlewood"
1188:-tuple occurs if the first condition but not necessarily the second condition is met.
1071:. (This structure is necessary to ensure that none of the six primes is divisible by
2209:
2184:
2162:
2142:
1765:
1737:
1430:
1287:
1209:
1206:
2119:
2104:
2041:
1755:
1658:
1275:
1060:{\displaystyle \{210n+97,\ 210n+101,\ 210n+103,\ 210n+107,\ 210n+109,\ 210n+113\}}
1820:
1780:
1663:
1628:
1592:
1547:
1400:
1388:
2225:
2199:
2096:
1964:
1815:
1775:
1760:
1632:
1523:
1488:
1443:
1368:
1350:
1279:
260:
The constant representing the sum of the reciprocals of all prime quadruplets,
2580:
2235:
2000:
1864:
1837:
1673:
1538:
1476:
1467:
1452:
1415:
1341:
1230:
1131:
207:
20:
2556:
2551:
2546:
2541:
2536:
2531:
2526:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2471:
2466:
2461:
2456:
2451:
2446:
2441:
2436:
2431:
2426:
2421:
2416:
2411:
2406:
2401:
2396:
2391:
2386:
2189:
1912:
1678:
1668:
1653:
1648:
1612:
1326:
544:
515:
133:
129:
125:
121:
114:
110:
106:
102:
32:
2381:
2376:
2371:
2366:
2361:
2356:
2351:
2346:
2341:
2336:
2331:
2326:
2321:
2316:
2311:
2306:
2301:
2296:
2291:
2286:
2281:
2127:
1800:
1708:
1703:
1683:
1597:
1500:
1376:
1236:
95:
91:
84:
80:
2204:
2020:
1928:
1848:
1698:
1602:
1295:
211:
203:
76:
72:
2245:
2194:
2075:
1214:
1270:
543:
The prime quadruplet {11, 13, 17, 19} is alleged to appear on the
1747:
1742:
1728:
202:
A prime quadruplet can be described as a consecutive pair of
893:
796:
738:
610:
238:
152:
273:, is the sum of the reciprocals of all prime quadruplets:
1204:
904:
a prime sextuplet. Our definition, all cases of primes
600: = 30. The first occurrences of this are for
2276:
2271:
2266:
2261:
948:
604:= 1006301, 2594951, 3919211, 9600551, 10531061, ... (
281:
1059:
486:
1140:-tuples. A prime constellation is a grouping of
2578:
1958: = 0, 1, 2, 3, ...
1258:Computational Methods in Science and Technology
512:This constant should not be confused with the
1311:
1054:
949:
886:{43777, 43781, 43783, 43787, 43789, 43793}
883:{19417, 19421, 19423, 19427, 19429, 19433},
880:{16057, 16061, 16063, 16067, 16069, 16073},
687:is also prime, then the five primes form a
1318:
1304:
1269:
1325:
1158:, meeting the following two conditions:
16:Set of prime numbers {p, p+2, p+6, p+8}
1836:
67:The first eight prime quadruplets are:
2579:
1299:
1205:
1248:
1119:
840:
788:{88807, 88811, 88813, 88817, 88819}
785:{79687, 79691, 79693, 79697, 79699},
782:{43777, 43781, 43783, 43787, 43789},
779:{19417, 19421, 19423, 19427, 19429},
776:{16057, 16061, 16063, 16067, 16069},
773:{15727, 15731, 15733, 15737, 15739},
730:{55331, 55333, 55337, 55339, 55343}
727:{43781, 43783, 43787, 43789, 43793},
724:{22271, 22273, 22277, 22279, 22283},
721:{21011, 21013, 21017, 21019, 21023},
718:{19421, 19423, 19427, 19429, 19433},
715:{16061, 16063, 16067, 16069, 16073},
648:
642:
62:
846:
808:infinitely many prime quintuplets.
13:
264:for prime quadruplets, denoted by
14:
2603:
1125:
746:The first prime quintuplets with
2592:Unsolved problems in mathematics
1694:Supersingular (moonshine theory)
508:= 0.87058 83800 ± 0.00000 00005.
770:{5647, 5651, 5653, 5657, 5659},
767:{3457, 3461, 3463, 3467, 3469},
764:{1867, 1871, 1873, 1877, 1879},
712:{1481, 1483, 1487, 1489, 1493},
1689:Supersingular (elliptic curve)
1224:
1198:
1166:are represented for any prime
877:{97, 101, 103, 107, 109, 113},
1:
1470:2 ± 2 ± 1
1191:
210:, or two intermixed pairs of
163:All prime quadruplets except
938:All prime sextuplets except
865:are prime then it becomes a
7:
1144:primes, with minimum prime
547:although this is disputed.
531:, which is also written as
10:
2608:
1280:10.12921/cmst.2019.0000033
1239:. Retrieved on 2019-02-28.
1232:The Top Twenty: Quadruplet
1129:
709:{101, 103, 107, 109, 113},
673:is a prime quadruplet and
519:, prime pairs of the form
206:, two overlapping sets of
2565:
2254:
2218:
2118:
2095:
2069:
1829:
1727:
1621:
1585:
1334:
761:{97, 101, 103, 107, 109},
257:, found by Peter Kaiser.
255:= 667674063382677 × 2 − 1
148:{2081, 2083, 2087, 2089}
145:{1871, 1873, 1877, 1879},
142:{1481, 1483, 1487, 1489},
2587:Classes of prime numbers
2076:Mega (1,000,000+ digits)
1945:Arithmetic progression (
1221:Retrieved on 2007-06-15.
1184:More generally, a prime
1162:Not all residues modulo
940:{7, 11, 13, 17, 19, 23}
874:{7, 11, 13, 17, 19, 23},
1180:is the minimum possible
902:{5, 7, 11, 13, 17, 19}
900:Some sources also call
2231:Industrial-grade prime
1608:Newman–Shanks–Williams
1061:
815:for prime quintuplets
621:for prime quadruplets
488:
225:digits in base 10 for
2568:List of prime numbers
2026:Sophie Germain/Safe (
1249:Tóth, László (2019),
1080:twin prime conjecture
1062:
706:{11, 13, 17, 19, 23},
489:
219:twin prime conjecture
139:{821, 823, 827, 829},
1750:(10 − 1)/9
946:
758:{7, 11, 13, 17, 19},
514:Brun's constant for
279:
2059: ± 7, ...
1586:By integer sequence
1371:(2 + 1)/3
703:{5, 7, 11, 13, 17},
57:prime constellation
31:) is a set of four
2241:Formula for primes
1874: + 2 or
1806:Smarandache–Wellin
1210:"Prime Quadruplet"
1207:Weisstein, Eric W.
1148:and maximum prime
1057:
484:
27:(sometimes called
2574:
2573:
2185:Carmichael number
2120:Composite numbers
2055: ± 3, 8
2051: ± 1, 4
2014: ± 1, …
2010: ± 1, 4
2006: ± 1, 2
1996:
1995:
1541:3·2 − 1
1446:2·3 + 1
1360:Double Mersenne (
1118:is 251331775687 (
1067:for some integer
1041:
1023:
1005:
987:
969:
942:are of the form
869:. The first few:
649:Prime quintuplets
471:
458:
445:
432:
409:
396:
383:
370:
347:
334:
321:
308:
187:for some integer
63:Prime quadruplets
2599:
2105:Eisenstein prime
2060:
2036:
2015:
1987:
1959:
1939:
1923:
1907:
1902: + 6,
1898: + 2,
1883:
1878: + 4,
1859:
1834:
1833:
1751:
1714:Highly cototient
1576:
1575:
1569:
1559:
1542:
1533:
1518:
1495:
1494:·2 − 1
1483:
1482:·2 + 1
1471:
1462:
1447:
1438:
1425:
1410:
1395:
1383:
1382:·2 + 1
1372:
1363:
1354:
1345:
1320:
1313:
1306:
1297:
1296:
1290:
1273:
1255:
1240:
1228:
1222:
1220:
1219:
1202:
1187:
1179:
1175:
1169:
1165:
1157:
1147:
1143:
1139:
1117:
1074:
1070:
1066:
1064:
1063:
1058:
1039:
1021:
1003:
985:
967:
941:
931:
903:
896:
887:
884:
881:
878:
875:
864:
857:
847:Prime sextuplets
838:
799:
789:
786:
783:
780:
777:
774:
771:
768:
765:
762:
759:
752:
741:
731:
728:
725:
722:
719:
716:
713:
710:
707:
704:
697:
689:prime quintuplet
686:
679:
672:
640:
613:
603:
599:
589:
569:
539:
530:
507:
493:
491:
490:
485:
477:
473:
472:
464:
459:
451:
446:
438:
433:
425:
415:
411:
410:
402:
397:
389:
384:
376:
371:
363:
353:
349:
348:
340:
335:
327:
322:
314:
309:
301:
291:
290:
272:
256:
254:
241:
231:
229:
224:
190:
186:
167:are of the form
166:
155:
149:
146:
143:
140:
137:
118:
99:
88:
54:
25:prime quadruplet
2607:
2606:
2602:
2601:
2600:
2598:
2597:
2596:
2577:
2576:
2575:
2570:
2561:
2255:First 60 primes
2250:
2214:
2114:
2097:Complex numbers
2091:
2065:
2043:
2027:
2002:
2001:Bi-twin chain (
1992:
1966:
1946:
1930:
1914:
1890:
1866:
1850:
1825:
1811:Strobogrammatic
1749:
1723:
1617:
1581:
1573:
1567:
1566:
1549:
1540:
1525:
1502:
1490:
1478:
1469:
1454:
1445:
1432:
1424:# + 1
1422:
1417:
1409:# ± 1
1407:
1402:
1394:! ± 1
1390:
1378:
1370:
1362:2 − 1
1361:
1353:2 − 1
1352:
1344:2 + 1
1343:
1330:
1324:
1294:
1253:
1244:
1243:
1229:
1225:
1203:
1199:
1194:
1185:
1177:
1176:, the value of
1173:
1167:
1163:
1149:
1145:
1141:
1137:
1134:
1128:
1091:
1090:for the tuplet
1072:
1068:
947:
944:
943:
939:
905:
901:
888:
885:
882:
879:
876:
873:
867:prime sextuplet
859:
852:
849:
816:
791:
787:
784:
781:
778:
775:
772:
769:
766:
763:
760:
757:
747:
733:
729:
726:
723:
720:
717:
714:
711:
708:
705:
702:
692:
681:
674:
654:
651:
622:
605:
601:
591:
571:
551:
538:
532:
520:
506:
500:
463:
450:
437:
424:
423:
419:
401:
388:
375:
362:
361:
357:
339:
326:
313:
300:
299:
295:
286:
282:
280:
277:
276:
271:
265:
262:Brun's constant
252:
251:
237:
227:
226:
222:
188:
168:
165:{5, 7, 11, 13}
164:
151:
147:
144:
141:
138:
119:
100:
89:
70:
65:
36:
29:prime quadruple
17:
12:
11:
5:
2605:
2595:
2594:
2589:
2572:
2571:
2566:
2563:
2562:
2560:
2559:
2554:
2549:
2544:
2539:
2534:
2529:
2524:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2484:
2479:
2474:
2469:
2464:
2459:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2419:
2414:
2409:
2404:
2399:
2394:
2389:
2384:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2344:
2339:
2334:
2329:
2324:
2319:
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2279:
2274:
2269:
2264:
2258:
2256:
2252:
2251:
2249:
2248:
2243:
2238:
2233:
2228:
2226:Probable prime
2222:
2220:
2219:Related topics
2216:
2215:
2213:
2212:
2207:
2202:
2200:Sphenic number
2197:
2192:
2187:
2182:
2181:
2180:
2175:
2170:
2165:
2160:
2155:
2150:
2145:
2140:
2135:
2124:
2122:
2116:
2115:
2113:
2112:
2110:Gaussian prime
2107:
2101:
2099:
2093:
2092:
2090:
2089:
2088:
2078:
2073:
2071:
2067:
2066:
2064:
2063:
2039:
2035: + 1
2023:
2018:
1997:
1994:
1993:
1991:
1990:
1962:
1942:
1938: + 6
1926:
1922: + 4
1910:
1906: + 8
1886:
1882: + 6
1862:
1858: + 2
1845:
1843:
1831:
1827:
1826:
1824:
1823:
1818:
1813:
1808:
1803:
1798:
1793:
1788:
1783:
1778:
1773:
1768:
1763:
1758:
1753:
1745:
1740:
1734:
1732:
1725:
1724:
1722:
1721:
1716:
1711:
1706:
1701:
1696:
1691:
1686:
1681:
1676:
1671:
1666:
1661:
1656:
1651:
1646:
1641:
1636:
1625:
1623:
1619:
1618:
1616:
1615:
1610:
1605:
1600:
1595:
1589:
1587:
1583:
1582:
1580:
1579:
1562:
1558: − 1
1545:
1536:
1521:
1498:
1486:
1474:
1465:
1450:
1441:
1437: + 1
1428:
1420:
1413:
1405:
1398:
1386:
1374:
1366:
1357:
1348:
1338:
1336:
1332:
1331:
1323:
1322:
1315:
1308:
1300:
1293:
1292:
1245:
1242:
1241:
1223:
1196:
1195:
1193:
1190:
1182:
1181:
1172:For any given
1170:
1130:Main article:
1127:
1126:Prime k-tuples
1124:
1056:
1053:
1050:
1047:
1044:
1038:
1035:
1032:
1029:
1026:
1020:
1017:
1014:
1011:
1008:
1002:
999:
996:
993:
990:
984:
981:
978:
975:
972:
966:
963:
960:
957:
954:
951:
898:
897:
848:
845:
802:
801:
744:
743:
650:
647:
536:
510:
509:
504:
483:
480:
476:
470:
467:
462:
457:
454:
449:
444:
441:
436:
431:
428:
422:
418:
414:
408:
405:
400:
395:
392:
387:
382:
379:
374:
369:
366:
360:
356:
352:
346:
343:
338:
333:
330:
325:
320:
317:
312:
307:
304:
298:
294:
289:
285:
269:
248:
247:
230:= 2, 3, 4, ...
208:prime triplets
64:
61:
15:
9:
6:
4:
3:
2:
2604:
2593:
2590:
2588:
2585:
2584:
2582:
2569:
2564:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2523:
2520:
2518:
2515:
2513:
2510:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2348:
2345:
2343:
2340:
2338:
2335:
2333:
2330:
2328:
2325:
2323:
2320:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2268:
2265:
2263:
2260:
2259:
2257:
2253:
2247:
2244:
2242:
2239:
2237:
2236:Illegal prime
2234:
2232:
2229:
2227:
2224:
2223:
2221:
2217:
2211:
2208:
2206:
2203:
2201:
2198:
2196:
2193:
2191:
2188:
2186:
2183:
2179:
2176:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2149:
2146:
2144:
2141:
2139:
2136:
2134:
2131:
2130:
2129:
2126:
2125:
2123:
2121:
2117:
2111:
2108:
2106:
2103:
2102:
2100:
2098:
2094:
2087:
2084:
2083:
2082:
2081:Largest known
2079:
2077:
2074:
2072:
2068:
2062:
2058:
2054:
2050:
2046:
2040:
2038:
2034:
2030:
2024:
2022:
2019:
2017:
2013:
2009:
2005:
1999:
1998:
1989:
1986:
1983: +
1982:
1978:
1974:
1971: −
1970:
1963:
1961:
1957:
1953:
1950: +
1949:
1943:
1941:
1937:
1933:
1927:
1925:
1921:
1917:
1911:
1909:
1905:
1901:
1897:
1893:
1887:
1885:
1881:
1877:
1873:
1869:
1863:
1861:
1857:
1853:
1847:
1846:
1844:
1842:
1840:
1835:
1832:
1828:
1822:
1819:
1817:
1814:
1812:
1809:
1807:
1804:
1802:
1799:
1797:
1794:
1792:
1789:
1787:
1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1757:
1754:
1752:
1746:
1744:
1741:
1739:
1736:
1735:
1733:
1730:
1726:
1720:
1717:
1715:
1712:
1710:
1707:
1705:
1702:
1700:
1697:
1695:
1692:
1690:
1687:
1685:
1682:
1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1634:
1630:
1627:
1626:
1624:
1620:
1614:
1611:
1609:
1606:
1604:
1601:
1599:
1596:
1594:
1591:
1590:
1588:
1584:
1578:
1572:
1563:
1561:
1557:
1553:
1546:
1544:
1537:
1535:
1532:
1529: +
1528:
1522:
1520:
1517:
1514: −
1513:
1509:
1506: −
1505:
1499:
1497:
1493:
1487:
1485:
1481:
1475:
1473:
1466:
1464:
1461:
1458: +
1457:
1451:
1449:
1442:
1440:
1436:
1431:Pythagorean (
1429:
1427:
1423:
1414:
1412:
1408:
1399:
1397:
1393:
1387:
1385:
1381:
1375:
1373:
1367:
1365:
1358:
1356:
1349:
1347:
1340:
1339:
1337:
1333:
1328:
1321:
1316:
1314:
1309:
1307:
1302:
1301:
1298:
1289:
1285:
1281:
1277:
1272:
1267:
1263:
1259:
1252:
1247:
1246:
1238:
1234:
1233:
1227:
1217:
1216:
1211:
1208:
1201:
1197:
1189:
1171:
1161:
1160:
1159:
1156:
1152:
1133:
1132:Prime k-tuple
1123:
1121:
1115:
1111:
1107:
1103:
1099:
1095:
1089:
1088:Skewes number
1084:
1081:
1076:
1051:
1048:
1045:
1042:
1036:
1033:
1030:
1027:
1024:
1018:
1015:
1012:
1009:
1006:
1000:
997:
994:
991:
988:
982:
979:
976:
973:
970:
964:
961:
958:
955:
952:
936:
933:
929:
925:
921:
917:
913:
909:
895:
891:
872:
871:
870:
868:
862:
855:
844:
842:
839:is 21432401 (
836:
832:
828:
824:
820:
814:
813:Skewes number
809:
805:
798:
794:
756:
755:
754:
750:
740:
736:
701:
700:
699:
695:
690:
684:
677:
670:
666:
662:
658:
646:
644:
638:
634:
630:
626:
620:
619:Skewes number
615:
612:
608:
598:
594:
587:
583:
579:
575:
567:
563:
559:
555:
548:
546:
541:
535:
528:
524:
518:
517:
516:cousin primes
503:
499:
498:
497:
494:
481:
478:
474:
468:
465:
460:
455:
452:
447:
442:
439:
434:
429:
426:
420:
416:
412:
406:
403:
398:
393:
390:
385:
380:
377:
372:
367:
364:
358:
354:
350:
344:
341:
336:
331:
328:
323:
318:
315:
310:
305:
302:
296:
292:
287:
283:
274:
268:
263:
258:
245:
240:
235:
234:
233:
220:
215:
213:
209:
205:
200:
196:
194:
184:
180:
176:
172:
161:
159:
154:
135:
131:
127:
123:
116:
112:
108:
104:
97:
93:
86:
82:
78:
74:
68:
60:
59:of length 4.
58:
52:
48:
44:
40:
34:
33:prime numbers
30:
26:
22:
21:number theory
2190:Almost prime
2148:Euler–Jacobi
2056:
2052:
2048:
2044:
2042:Cunningham (
2032:
2028:
2011:
2007:
2003:
1984:
1980:
1976:
1972:
1968:
1967:consecutive
1955:
1951:
1947:
1935:
1931:
1919:
1915:
1903:
1899:
1895:
1891:
1889:Quadruplet (
1888:
1879:
1875:
1871:
1867:
1855:
1851:
1838:
1786:Full reptend
1644:Wolstenholme
1639:Wall–Sun–Sun
1570:
1555:
1551:
1530:
1526:
1515:
1511:
1507:
1503:
1491:
1479:
1459:
1455:
1434:
1418:
1403:
1391:
1379:
1327:Prime number
1261:
1257:
1231:
1226:
1213:
1200:
1183:
1154:
1150:
1135:
1113:
1109:
1105:
1101:
1097:
1093:
1085:
1077:
1073:2, 3, 5 or 7
937:
934:
927:
923:
919:
915:
911:
907:
899:
866:
860:
853:
850:
834:
830:
826:
822:
818:
810:
806:
803:
748:
745:
693:
688:
682:
675:
668:
664:
660:
656:
652:
641:is 1172531 (
636:
632:
628:
624:
616:
596:
592:
585:
581:
577:
573:
565:
561:
557:
553:
549:
545:Ishango bone
542:
533:
526:
522:
513:
511:
501:
496:with value:
495:
275:
266:
259:
249:
216:
201:
197:
193:prime decade
192:
182:
178:
174:
170:
162:
69:
66:
50:
46:
42:
38:
35:of the form
28:
24:
18:
2173:Somer–Lucas
2128:Pseudoprime
1766:Truncatable
1738:Palindromic
1622:By property
1401:Primorial (
1389:Factorial (
1237:Prime Pages
1120:Tóth (2019)
910:− 4,
841:Tóth (2019)
643:Tóth (2019)
212:sexy primes
204:twin primes
2581:Categories
2210:Pernicious
2205:Interprime
1965:Balanced (
1756:Permutable
1731:-dependent
1548:Williams (
1444:Pierpont (
1369:Wagstaff
1351:Mersenne (
1335:By formula
1271:1910.02636
1192:References
150:(sequence
2246:Prime gap
2195:Semiprime
2158:Frobenius
1865:Triplet (
1664:Ramanujan
1659:Fortunate
1629:Wieferich
1593:Fibonacci
1524:Leyland (
1489:Woodall (
1468:Solinas (
1453:Quartan (
1288:203836016
1215:MathWorld
856:− 4
751:− 4
678:− 4
482:⋯
90:{11, 13,
2138:Elliptic
1913:Cousin (
1830:Patterns
1821:Tetradic
1816:Dihedral
1781:Primeval
1776:Delicate
1761:Circular
1748:Repunit
1539:Thabit (
1477:Cullen (
1416:Euclid (
1342:Fermat (
851:If both
181:+ 17, 30
177:+ 13, 30
173:+ 11, 30
2133:Catalan
2070:By size
1841:-tuples
1771:Minimal
1674:Regular
1565:Mills (
1501:Cuban (
1377:Proth (
1329:classes
1235:at The
894:A022008
892::
797:A022007
795::
739:A022006
737::
611:A059925
609::
242:in the
239:A120120
156:in the
153:A007530
2178:Strong
2168:Perrin
2153:Fermat
1929:Sexy (
1849:Twin (
1791:Unique
1719:Unique
1679:Strong
1669:Pillai
1649:Wilson
1613:Perrin
1286:
1116:+ 16}
1112:+ 12,
1108:+ 10,
1040:
1022:
1004:
986:
968:
930:+ 12},
837:+ 12}
185:+ 19}
2163:Lucas
2143:Euler
1796:Happy
1743:Emirp
1709:Higgs
1704:Super
1684:Stern
1654:Lucky
1598:Lucas
1284:S2CID
1266:arXiv
1264:(3),
1254:(PDF)
1104:+ 6,
1100:+ 4,
926:+ 8,
922:+ 6,
918:+ 2,
833:+ 8,
829:+ 6,
825:+ 2,
753:are:
698:are:
671:+ 8}
667:+ 6,
663:+ 2,
639:+ 8}
635:+ 6,
631:+ 2,
588:+ 8}
584:+ 6,
580:+ 2,
568:+ 8}
564:+ 6,
560:+ 2,
53:+ 8}.
49:+ 6,
45:+ 2,
2086:list
2021:Chen
1801:Self
1729:Base
1699:Good
1633:pair
1603:Pell
1554:−1)·
1086:The
890:OEIS
863:+ 12
858:and
811:The
793:OEIS
790:...
735:OEIS
696:+ 12
685:+ 12
617:The
607:OEIS
590:is
570:and
529:+ 4)
244:OEIS
232:is
158:OEIS
23:, a
2557:281
2552:277
2547:271
2542:269
2537:263
2532:257
2527:251
2522:241
2517:239
2512:233
2507:229
2502:227
2497:223
2492:211
2487:199
2482:197
2477:193
2472:191
2467:181
2462:179
2457:173
2452:167
2447:163
2442:157
2437:151
2432:149
2427:139
2422:137
2417:131
2412:127
2407:113
2402:109
2397:107
2392:103
2387:101
2047:, 2
2031:, 2
1952:a·n
1510:)/(
1276:doi
1122:).
1075:).
1052:113
1043:210
1034:109
1025:210
1016:107
1007:210
998:103
989:210
980:101
971:210
953:210
843:).
680:or
653:If
645:).
614:).
469:109
456:107
443:103
430:101
169:{30
134:199
130:197
126:193
122:191
115:109
111:107
107:103
103:101
19:In
2583::
2382:97
2377:89
2372:83
2367:79
2362:73
2357:71
2352:67
2347:61
2342:59
2337:53
2332:47
2327:43
2322:41
2317:37
2312:31
2307:29
2302:23
2297:19
2292:17
2287:13
2282:11
1979:,
1975:,
1954:,
1934:,
1918:,
1894:,
1870:,
1854:,
1282:,
1274:,
1262:25
1260:,
1256:,
1212:.
1153:+
1096:,
962:97
914:,
821:,
732:…
659:,
627:,
595:-
576:,
556:,
540:.
525:,
407:19
394:17
381:13
368:11
345:13
332:11
246:).
195:.
160:)
136:},
132:,
128:,
124:,
117:},
113:,
109:,
105:,
98:},
96:19
94:,
92:17
87:},
85:13
83:,
81:11
79:,
75:,
41:,
2277:7
2272:5
2267:3
2262:2
2061:)
2057:p
2053:p
2049:p
2045:p
2037:)
2033:p
2029:p
2016:)
2012:n
2008:n
2004:n
1988:)
1985:n
1981:p
1977:p
1973:n
1969:p
1960:)
1956:n
1948:p
1940:)
1936:p
1932:p
1924:)
1920:p
1916:p
1908:)
1904:p
1900:p
1896:p
1892:p
1884:)
1880:p
1876:p
1872:p
1868:p
1860:)
1856:p
1852:p
1839:k
1635:)
1631:(
1577:)
1574:⌋
1571:A
1568:⌊
1560:)
1556:b
1552:b
1550:(
1543:)
1534:)
1531:y
1527:x
1519:)
1516:y
1512:x
1508:y
1504:x
1496:)
1492:n
1484:)
1480:n
1472:)
1463:)
1460:y
1456:x
1448:)
1439:)
1435:n
1433:4
1426:)
1421:n
1419:p
1411:)
1406:n
1404:p
1396:)
1392:n
1384:)
1380:k
1364:)
1355:)
1346:)
1319:e
1312:t
1305:v
1291:.
1278::
1268::
1218:.
1186:k
1178:n
1174:k
1168:q
1164:q
1155:n
1151:p
1146:p
1142:k
1138:k
1114:p
1110:p
1106:p
1102:p
1098:p
1094:p
1092:{
1069:n
1055:}
1049:+
1046:n
1037:,
1031:+
1028:n
1019:,
1013:+
1010:n
1001:,
995:+
992:n
983:,
977:+
974:n
965:,
959:+
956:n
950:{
928:p
924:p
920:p
916:p
912:p
908:p
906:{
861:p
854:p
835:p
831:p
827:p
823:p
819:p
817:{
800:.
749:p
742:.
694:p
683:p
676:p
669:p
665:p
661:p
657:p
655:{
637:p
633:p
629:p
625:p
623:{
602:p
597:p
593:q
586:q
582:q
578:q
574:q
572:{
566:p
562:p
558:p
554:p
552:{
537:4
534:B
527:p
523:p
521:(
505:4
502:B
479:+
475:)
466:1
461:+
453:1
448:+
440:1
435:+
427:1
421:(
417:+
413:)
404:1
399:+
391:1
386:+
378:1
373:+
365:1
359:(
355:+
351:)
342:1
337:+
329:1
324:+
319:7
316:1
311:+
306:5
303:1
297:(
293:=
288:4
284:B
270:4
267:B
253:p
228:n
223:n
189:n
183:n
179:n
175:n
171:n
120:{
101:{
77:7
73:5
71:{
51:p
47:p
43:p
39:p
37:{
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.