Prímszámok listája
Végtelen sok prímszám van. Az első lista az első 148 933-at tartalmazza, melyet a különböző nevezetes prímszámtípusok listái követnek ábécésorrendben.
A 2 milliónál kisebb prímszámok
A következő lista 148 933 prímszámot tartalmaz. Az oldal jobb átláthatósága érdekében a táblázat össze van csukva, a jobb oldali gombbal nyitható. |
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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, 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1981739, 1981753, 1981787, 1981813, 1981853, 1981867, 1981879, 1981883, 1981891, 1981901, 1981919, 1981921, 1981939, 1981949, 1981963, 1981997, 1982011, 1982021, 1982033, 1982051, 1982059, 1982069, 1982077, 1982083, 1982087, 1982093, 1982111, 1982129, 1982153, 1982159, 1982173, 1982191, 1982203, 1982207, 1982219, 1982263, 1982269, 1982273, 1982287, 1982291, 1982293, 1982371, 1982381, 1982401, 1982417, 1982437, 1982443, 1982447, 1982467, 1982471, 1982501, 1982509, 1982521, 1982537, 1982551, 1982567, 1982573, 1982579, 1982587, 1982599, 1982609, 1982611, 1982627, 1982633, 1982639, 1982641, 1982671, 1982681, 1982713, 1982723, 1982741, 1982779, 1982797, 1982803, 1982809, 1982833, 1982837, 1982839, 1982843, 1982857, 1982861, 1982873, 1982879, 1982881, 1982887, 1982891, 1982909, 1982917, 1982921, 1982951, 1982957, 1982969, 1982987, 1982989, 1982993, 1983001, 1983013, 1983019, 1983053, 1983061, 1983077, 1983097, 1983103, 1983109, 1983143, 1983197, 1983227, 1983229, 1983253, 1983257, 1983301, 1983323, 1983341, 1983343, 1983347, 1983361, 1983379, 1983383, 1983389, 1983409, 1983413, 1983427, 1983437, 1983439, 1983463, 1983479, 1983491, 1983493, 1983503, 1983523, 1983559, 1983563, 1983587, 1983599, 1983601, 1983643, 1983647, 1983649, 1983689, 1983697, 1983701, 1983731, 1983743, 1983749, 1983763, 1983767, 1983833, 1983851, 1983853, 1983859, 1983871, 1983881, 1983889, 1983913, 1983929, 1983931, 1983967, 1983979, 1983997, 1984007, 1984013, 1984039, 1984043, 1984057, 1984061, 1984069, 1984079, 1984091, 1984109, 1984117, 1984123, 1984133, 1984139, 1984159, 1984163, 1984181, 1984183, 1984201, 1984211, 1984247, 1984259, 1984261, 1984271, 1984309, 1984319, 1984327, 1984331, 1984337, 1984343, 1984351, 1984361, 1984363, 1984397, 1984399, 1984429, 1984453, 1984457, 1984459, 1984471, 1984511, 1984537, 1984547, 1984561, 1984571, 1984639, 1984649, 1984667, 1984709, 1984711, 1984727, 1984729, 1984747, 1984753, 1984777, 1984783, 1984793, 1984799, 1984813, 1984817, 1984841, 1984849, 1984859, 1984867, 1984891, 1984897, 1984901, 1984907, 1984921, 1984979, 1984981, 1984991, 1985003, 1985017, 1985041, 1985047, 1985051, 1985057, 1985077, 1985167, 1985183, 1985189, 1985213, 1985219, 1985227, 1985237, 1985239, 1985257, 1985279, 1985287, 1985293, 1985303, 1985317, 1985363, 1985377, 1985407, 1985419, 1985441, 1985453, 1985471, 1985483, 1985491, 1985509, 1985513, 1985537, 1985551, 1985561, 1985573, 1985587, 1985591, 1985593, 1985623, 1985639, 1985663, 1985677, 1985689, 1985713, 1985729, 1985741, 1985743, 1985759, 1985771, 1985779, 1985791, 1985803, 1985849, 1985873, 1985887, 1985897, 1985903, 1985939, 1985987, 1985989, 1986001, 1986029, 1986037, 1986043, 1986053, 1986067, 1986071, 1986097, 1986109, 1986121, 1986133, 1986137, 1986167, 1986169, 1986199, 1986217, 1986223, 1986233, 1986253, 1986277, 1986289, 1986293, 1986301, 1986311, 1986323, 1986337, 1986359, 1986373, 1986401, 1986421, 1986437, 1986443, 1986461, 1986497, 1986499, 1986527, 1986539, 1986541, 1986547, 1986553, 1986577, 1986581, 1986601, 1986629, 1986631, 1986679, 1986683, 1986689, 1986713, 1986749, 1986757, 1986769, 1986779, 1986781, 1986797, 1986823, 1986839, 1986869, 1986871, 1986889, 1986893, 1986899, 1986913, 1986923, 1986949, 1986967, 1986989, 1986991, 1986997, 1987003, 1987031, 1987043, 1987049, 1987057, 1987067, 1987081, 1987091, 1987099, 1987121, 1987123, 1987127, 1987151, 1987157, 1987189, 1987201, 1987217, 1987231, 1987241, 1987247, 1987261, 1987277, 1987291, 1987303, 1987309, 1987313, 1987333, 1987339, 1987373, 1987411, 1987429, 1987439, 1987451, 1987471, 1987477, 1987481, 1987483, 1987501, 1987519, 1987523, 1987537, 1987543, 1987547, 1987549, 1987577, 1987619, 1987621, 1987649, 1987673, 1987679, 1987681, 1987693, 1987697, 1987703, 1987709, 1987789, 1987819, 1987829, 1987841, 1987849, 1987873, 1987879, 1987883, 1987889, 1987891, 1987901, 1987919, 1987939, 1987969, 1987981, 1987987, 1987991, 1988011, 1988023, 1988033, 1988057, 1988087, 1988089, 1988101, 1988113, 1988137, 1988177, 1988183, 1988197, 1988219, 1988221, 1988227, 1988237, 1988243, 1988249, 1988251, 1988257, 1988263, 1988267, 1988279, 1988291, 1988297, 1988299, 1988323, 1988339, 1988341, 1988347, 1988353, 1988411, 1988423, 1988453, 1988471, 1988513, 1988531, 1988533, 1988537, 1988549, 1988551, 1988561, 1988563, 1988579, 1988587, 1988599, 1988611, 1988633, 1988653, 1988659, 1988669, 1988671, 1988683, 1988689, 1988699, 1988729, 1988759, 1988797, 1988801, 1988807, 1988837, 1988839, 1988843, 1988851, 1988887, 1988891, 1988897, 1988933, 1988941, 1988963, 1988999, 1989007, 1989019, 1989049, 1989059, 1989073, 1989077, 1989101, 1989107, 1989131, 1989133, 1989151, 1989161, 1989193, 1989203, 1989217, 1989233, 1989241, 1989259, 1989263, 1989277, 1989307, 1989329, 1989341, 1989353, 1989401, 1989413, 1989419, 1989479, 1989499, 1989517, 1989551, 1989553, 1989563, 1989571, 1989583, 1989613, 1989619, 1989643, 1989671, 1989679, 1989683, 1989721, 1989769, 1989787, 1989791, 1989803, 1989811, 1989847, 1989863, 1989877, 1989899, 1989919, 1989947, 1989959, 1989961, 1989973, 1989979, 1989989, 1990007, 1990031, 1990033, 1990039, 1990069, 1990081, 1990103, 1990111, 1990123, 1990133, 1990141, 1990147, 1990151, 1990159, 1990171, 1990187, 1990189, 1990211, 1990223, 1990229, 1990237, 1990243, 1990249, 1990253, 1990273, 1990277, 1990279, 1990319, 1990321, 1990327, 1990337, 1990361, 1990379, 1990381, 1990433, 1990441, 1990447, 1990453, 1990463, 1990481, 1990487, 1990493, 1990507, 1990523, 1990529, 1990543, 1990553, 1990559, 1990577, 1990579, 1990607, 1990621, 1990643, 1990657, 1990661, 1990679, 1990691, 1990693, 1990753, 1990759, 1990787, 1990823, 1990829, 1990831, 1990867, 1990871, 1990883, 1990889, 1990907, 1990927, 1990939, 1990951, 1990957, 1990969, 1990973, 1990981, 1990987, 1991027, 1991047, 1991063, 1991071, 1991089, 1991107, 1991123, 1991131, 1991137, 1991147, 1991153, 1991177, 1991189, 1991239, 1991243, 1991251, 1991267, 1991279, 1991281, 1991293, 1991351, 1991357, 1991359, 1991387, 1991389, 1991413, 1991443, 1991449, 1991461, 1991477, 1991489, 1991491, 1991503, 1991519, 1991527, 1991551, 1991573, 1991597, 1991603, 1991609, 1991617, 1991623, 1991641, 1991653, 1991677, 1991681, 1991707, 1991723, 1991729, 1991753, 1991761, 1991779, 1991797, 1991819, 1991837, 1991849, 1991861, 1991863, 1991879, 1991881, 1991893, 1991911, 1991921, 1991929, 1991933, 1991947, 1991959, 1991963, 1991989, 1991993, 1991999, 1992031, 1992041, 1992049, 1992073, 1992079, 1992101, 1992119, 1992139, 1992163, 1992167, 1992181, 1992197, 1992203, 1992227, 1992241, 1992251, 1992257, 1992259, 1992269, 1992299, 1992307, 1992337, 1992343, 1992373, 1992407, 1992409, 1992433, 1992437, 1992439, 1992469, 1992481, 1992493, 1992509, 1992517, 1992527, 1992533, 1992547, 1992563, 1992583, 1992589, 1992611, 1992623, 1992631, 1992637, 1992643, 1992673, 1992691, 1992713, 1992719, 1992733, 1992761, 1992763, 1992769, 1992779, 1992797, 1992803, 1992817, 1992839, 1992841, 1992877, 1992883, 1992889, 1992911, 1992917, 1992919, 1992937, 1992953, 1992971, 1992983, 1993031, 1993037, 1993039, 1993067, 1993087, 1993109, 1993127, 1993151, 1993163, 1993193, 1993217, 1993219, 1993231, 1993237, 1993241, 1993247, 1993259, 1993261, 1993273, 1993289, 1993307, 1993319, 1993339, 1993349, 1993357, 1993363, 1993367, 1993417, 1993441, 1993457, 1993477, 1993483, 1993493, 1993507, 1993513, 1993529, 1993531, 1993553, 1993561, 1993591, 1993601, 1993603, 1993627, 1993631, 1993633, 1993637, 1993643, 1993657, 1993661, 1993679, 1993681, 1993687, 1993697, 1993699, 1993711, 1993729, 1993757, 1993759, 1993763, 1993829, 1993861, 1993877, 1993921, 1993931, 1993933, 1993949, 1993963, 1993969, 1993973, 1993991, 1993997, 1994033, 1994051, 1994053, 1994059, 1994081, 1994087, 1994093, 1994101, 1994119, 1994143, 1994191, 1994203, 1994207, 1994227, 1994299, 1994327, 1994339, 1994341, 1994347, 1994357, 1994381, 1994387, 1994413, 1994429, 1994437, 1994441, 1994459, 1994467, 1994471, 1994477, 1994479, 1994483, 1994497, 1994501, 1994519, 1994521, 1994543, 1994567, 1994569, 1994599, 1994621, 1994623, 1994647, 1994651, 1994659, 1994669, 1994687, 1994711, 1994717, 1994743, 1994777, 1994779, 1994807, 1994827, 1994833, 1994843, 1994869, 1994879, 1994897, 1994911, 1994947, 1994953, 1994959, 1994977, 1994983, 1994989, 1995011, 1995013, 1995023, 1995031, 1995061, 1995073, 1995083, 1995107, 1995109, 1995121, 1995139, 1995143, 1995187, 1995211, 1995221, 1995223, 1995263, 1995271, 1995289, 1995293, 1995311, 1995317, 1995337, 1995349, 1995353, 1995359, 1995391, 1995421, 1995431, 1995449, 1995473, 1995481, 1995517, 1995527, 1995529, 1995533, 1995541, 1995547, 1995583, 1995607, 1995611, 1995629, 1995649, 1995661, 1995677, 1995683, 1995689, 1995691, 1995709, 1995713, 1995727, 1995769, 1995781, 1995787, 1995797, 1995827, 1995841, 1995857, 1995869, 1995883, 1995913, 1995937, 1995947, 1995967, 1995971, 1995977, 1995979, 1995989, 1995991, 1996013, 1996019, 1996061, 1996081, 1996087, 1996091, 1996097, 1996109, 1996129, 1996171, 1996177, 1996207, 1996217, 1996219, 1996223, 1996229, 1996237, 1996277, 1996279, 1996283, 1996289, 1996297, 1996301, 1996303, 1996321, 1996333, 1996343, 1996363, 1996381, 1996391, 1996403, 1996411, 1996417, 1996427, 1996439, 1996453, 1996459, 1996471, 1996481, 1996487, 1996507, 1996517, 1996529, 1996543, 1996549, 1996559, 1996573, 1996583, 1996609, 1996613, 1996639, 1996649, 1996681, 1996697, 1996711, 1996717, 1996721, 1996723, 1996739, 1996751, 1996759, 1996763, 1996777, 1996781, 1996793, 1996817, 1996829, 1996849, 1996859, 1996867, 1996879, 1996901, 1996903, 1996933, 1996937, 1996949, 1996979, 1997003, 1997029, 1997053, 1997057, 1997059, 1997081, 1997087, 1997089, 1997101, 1997111, 1997119, 1997129, 1997137, 1997141, 1997161, 1997173, 1997179, 1997183, 1997189, 1997213, 1997231, 1997243, 1997257, 1997267, 1997269, 1997293, 1997311, 1997321, 1997339, 1997341, 1997351, 1997407, 1997419, 1997431, 1997441, 1997459, 1997467, 1997473, 1997503, 1997507, 1997531, 1997539, 1997543, 1997557, 1997587, 1997591, 1997599, 1997617, 1997647, 1997657, 1997663, 1997683, 1997693, 1997701, 1997707, 1997713, 1997719, 1997731, 1997747, 1997753, 1997771, 1997773, 1997813, 1997833, 1997843, 1997851, 1997867, 1997887, 1997899, 1997903, 1997911, 1997921, 1997939, 1997969, 1997999, 1998019, 1998023, 1998041, 1998049, 1998067, 1998077, 1998089, 1998107, 1998109, 1998119, 1998127, 1998133, 1998169, 1998181, 1998209, 1998221, 1998223, 1998233, 1998251, 1998257, 1998277, 1998289, 1998301, 1998319, 1998329, 1998331, 1998341, 1998343, 1998349, 1998371, 1998379, 1998397, 1998413, 1998427, 1998431, 1998443, 1998449, 1998457, 1998473, 1998497, 1998517, 1998527, 1998533, 1998541, 1998559, 1998569, 1998587, 1998589, 1998611, 1998617, 1998637, 1998641, 1998643, 1998679, 1998691, 1998697, 1998701, 1998727, 1998739, 1998761, 1998793, 1998817, 1998827, 1998839, 1998881, 1998917, 1998923, 1998943, 1998947, 1998949, 1998961, 1998977, 1998991, 1999007, 1999021, 1999033, 1999043, 1999061, 1999069, 1999099, 1999103, 1999111, 1999121, 1999163, 1999177, 1999187, 1999211, 1999219, 1999223, 1999243, 1999247, 1999273, 1999297, 1999301, 1999303, 1999307, 1999331, 1999339, 1999343, 1999363, 1999379, 1999423, 1999441, 1999471, 1999499, 1999511, 1999513, 1999537, 1999549, 1999559, 1999561, 1999567, 1999603, 1999607, 1999619, 1999631, 1999633, 1999651, 1999661, 1999667, 1999681, 1999691, 1999703, 1999721, 1999733, 1999771, 1999799, 1999817, 1999819, 1999853, 1999859, 1999867, 1999871, 1999889, 1999891, 1999957, 1999969, 1999979, 1999993 |
(A000040 sorozat az OEIS-ben)
Típus szerint
A következő listák több, névvel illetett prímszámalakot és prímszámtípust tartalmaznak.
A definíciókban n mindig természetes szám (beleértve a 0-t is).
Additív prímek
Olyan prímszámok, amelyek számjegyei összege is prím.[1]
2; 3; 5; 7; 11; 23; 29; 41; 43; 47; 61; 67; 83; 89; 101; 113; 131; 137; 139
Aranymetszésprímek
A prímszám aranymetszésprím, ha:
, ahol pozitív egész és , ahol pozitív egész és
vagy vagy és irracionális.
-re: 13, 47, 89, 131, 157, 191, 199, 233, 419, 479, 487 stb.
-re: 89, 233, 521, 1453, 1597, 1741, 2029 stb.
-re: 1597, 3571, 9349, 11933, 15737 stb.[2]
Bali-Stein-prímpárok
Olyan prímszámpárok, melyeknek 2-es számrendszerbeli alakján elvégezve a XOR műveletet, 2 valamely hatványát kapjuk. Más szavakkal a két prím különbségének eredménye 2 valamely hatványa.
(2-3); (3-7); (3-11); (3-19); (3-67); (17-19); (19-83); (83-2131); (101-613); (191-2239); (223-479); (577-1601); (719-2767); (839-2887); (1259-3307); (1301-1303); (1511-3559); (1997-2029); (2389-3413)...
Balogh-prímpárok
Az olyan három egymást követő ikerprímpárt, melyek között csak összetett számok vannak, Balogh-prímpároknak nevezünk.
(3-5;5-7;11-13); (5-7;11-13;17-19); (179-181;191-193;197-199); (3359-3361;3371-3373;3389-3391); (4217-4219;4229-4231;4241-4243); (6761-6763;6779-6781;6791-6793)...
Bell-prímek
Olyan Bell-számok, amelyek prímek.
2; 5; 877; 27644437; 35742549198872617291353508656626642567; 359334085968622831041960188598043661065388726959079837 (A051131 sorozat az OEIS-ben)
Biztonságos prímek
![]() | Bővebben: Biztonságos prímek |
Ahol és egyaránt prímek.
5; 7; 11; 23; 47; 59; 83; 107; 167; 179; 227; 263; 347; 359; 383; 467; 479; 503; 563; 587; 719; 839; 863; 887; 983; 1019; 1187; 1283; 1307; 1319; 1367; 1439; 1487; 1523; 1619; 1823; 1907 (A005385 sorozat az OEIS-ben)
Boldog prímek
Olyan boldog számok, amelyek prímek is.
7; 13; 19; 23; 31; 79; 97; 103; 109; 139; 167; 193; 239; 263; 293; 313; 331; 367; 379; 383; 397; 409; 487; 563; 617; 653; 673; 683; 709; 739; 761; 863; 881; 907; 937; 1009; 1033; 1039; 1093 (A035497 sorozat az OEIS-ben)
Bölcsföldi-prímek
Definíció:
Egy prímszám (tízes számrendszerben) Bölcsföldi-prím, ha:
- a) minden számjegye 2 vagy 3,
- b) a számjegyek száma prím,
- c) a számjegyek összege prím.
23, 223, 32233, 32323, 33223, 2222333, 2223233, 2232323, 2233223 stb.
Bölcsföldi prime numbers
International Journal of Engineering and Science Invention:
http://www.ijesi.org/v7i8(version-5).html
Bölcsföldi–Birkás-prímek
Olyan prímszámok, melyeknek:[3]
- a) minden számjegye prím (2, 3, 5 vagy 7),
- b) a számjegyek száma prím,
- c) a számjegyek összege is prím.
23, 223, 227, 337, 353, 373, 557, 577, 733, 757, 773, ...
Bölcsföldi–Birkás–Bíró monoton prímek
Definíció:
Egy prímszám (tízes számrendszerben) Bölcsföldi–Birkás–Bíró monoton növekvő prím, ha:
- a) a szám számjegyei monoton nőnek,
- b) a számjegyek száma prím,
- c) a számjegyek összege prím.
23, 223, 227, 337, 557, 577, 33377 stb.
Ugyanígy a monoton csökkenő prímek.
http://www.ijlemr.com/current%20issue.html
Bölcsföldi–Dömötör-prímek
Definíció:
Egy prímszám (tízes számrendszerben) Bölcsföldi–Dömötör-prím, ha:
- a) minden számjegye prím (2, 3, 5 vagy 7),
- b) a számjegyek száma prím,
- c) a számjegyek összege prím.[4]
23, 223, 353, 25253, 25523, 32233, 32323, 33223, 33353 stb.
Chen-prímek
p prím és p + 2 vagy prím vagy félprím, azaz két prímszám szorzata.
2; 3; 5; 7; 11; 13; 17; 19; 23; 29; 31; 37; 41; 47; 53; 59; 67; 71; 83; 89; 101; 107; 109; 113; 127; 131; 137; 139; 149; 157; 167; 179; 181; 191; 197; 199; 211; 227; 233; 239; 251; 257; 263; 269 (A109611 sorozat az OEIS-ben)
Csillagprímek
6n(n - 1) + 1 alakú prímszámok.
13; 37; 73; 181; 337; 433; 541; 661; 937; 1093; 2053; 2281; 2521; 3037; 3313; 5581; 5953; 6337; 6733; 7561; 7993; 8893; 10333; 10837; 11353; 12421; 12973; 13537; 15913; 18481 (A083577 sorozat az OEIS-ben)
Csonkolható prímek
Balról csonkolható prímek
Az olyan prímszámot nevezzük balról csonkolhatónak, amelynek (tízes számrendszerben) balról elhagyva a kezdő számjegyeit mindig prímet kapunk.
2; 3; 5; 7; 13; 17; 23; 37; 43; 47; 53; 67; 73; 83; 97; 113; 137; 167; 173; 197; 223; 283; 313; 317; 337; 347; 353; 367; 373; 383; 397; 443; 467; 523; 547; 613; 617; 643; 647; 653; 673; 683 (A024785 sorozat az OEIS-ben)
Jobbról csonkolható prímek
Az olyan prímszámot nevezzük jobbról csonkolhatónak, amelynek (tízes számrendszerben) jobbról elhagyva a záró számjegyeit mindig prímet kapunk.
2; 3; 5; 7; 23; 29; 31; 37; 53; 59; 71; 73; 79; 233; 239; 293; 311; 313; 317; 373; 379; 593; 599; 719; 733; 739; 797; 2333; 2339; 2393; 2399; 2939; 3119; 3137; 3733; 3739; 3793; 3797 (A024770 sorozat az OEIS-ben)
Dupla Mersenne-prímek
![]() | Bővebben: Mersenne-prímek |
Olyan alakú prím, ahol p is prím.
7; 127; 2147483647; 170141183460469231731687303715884105727
2008 januárjában összesen ezek a dupla Mersenne-prímek ismertek. Figyelem, a dupla Mersenne-prím a Mersenne-prím speciális esete!
Eisenstein-prímek
Olyan irreducibilis elemek a Eisenstein-egészek körében, amelyeknek az imaginárius része nulla (a számok felírhatók 3n+2 alakban).
2; 5; 11; 17; 23; 29; 41; 47; 53; 59; 71; 83; 89; 101; 107; 113; 131; 137; 149; 167; 173; 179; 191; 197; 227; 233; 239; 251; 257; 263; 269; 281; 293; 311; 317; 347; 353; 359; 383; 389; 401 (A003627 sorozat az OEIS-ben)
Erdős-prímek
Olyan prímek, melyekre tetszőleges esetén nem prím.
Első elemeik: 2; 101; 367; 409; 419; 467[5]
Euklideszi prímek
Prímek, melyek Eukleidész-féle számok.
2; 3; 7; 31; 211; 2311; 200560490131 (A018239 sorozat az OEIS-ben)
Faktoriális prímek
n!±1 alakú prímszámok.
2; 3; 5; 7; 23; 719; 5039; 39916801; 479001599; 87178291199; 10888869450418352160768000001; 265252859812191058636308479999999; 263130836933693530167218012159999999; 8683317618811886495518194401279999999 (A088054 sorozat az OEIS-ben)
Fermat-prímek
![]() | Bővebben: Fermat-prímek |
![]() | Bővebben: Fermat-számok |
Olyan prímek, melyek Fermat-számok, tehát alakú prímszámok.
3; 5; 17; 257; 65537 (A019434 sorozat az OEIS-ben)
2016 decemberében csak ezek a Fermat-prímek ismertek.
Fibonacci-prímek
![]() | Bővebben: Fibonacci-prímek |
![]() | Bővebben: Fibonacci-számok |
Prímek a Fibonacci-sorozatban: F0 = 0; F1 = 1; Fn = Fn-1 + Fn-2.
2; 3; 5; 13; 89; 233; 1597; 28657; 514229; 433494437; 2971215073; 99194853094755497; 1066340417491710595814572169; 19134702400093278081449423917 (A005478 sorozat az OEIS-ben)
Gauss-prímek
![]() | Bővebben: Gauss-egészek |
A Gauss-egészek racionális prím elemei (4n + 3 alakú prímek).
3; 7; 11; 19; 23; 31; 43; 47; 59; 67; 71; 79; 83; 103; 107; 127; 131; 139; 151; 163; 167; 179; 191; 199; 211; 223; 227; 239; 251; 263; 271; 283; 307; 311; 331; 347; 359; 367; 379; 383; 419; 431; 439; 443; 463; 467; 479; 487; 491; 499; 503 (A002145 sorozat az OEIS-ben)
Genocchi-prímek
Az egyetlen pozitív Genocchi-prím a 17.
Ikerprímek
(p; p + 2) prím párok.
(3; 5); (5; 7); (11; 13); (17; 19); (29; 31); (41; 43); (59; 61); (71; 73); (101; 103); (107; 109); (137; 139); (149; 151); (179; 181); (191; 193); (197; 199); (227; 229); (239; 241); (269; 271); (281; 283); (311; 313); (347; 349); (419; 421); (431; 433); (461; 463); (521;523); (569;571); (A001359 sorozat az OEIS-ben); (A006512 sorozat az OEIS-ben)
Kiegyensúlyozott prímek
Olyan prímszámok, melyek azonos távolságra vannak a két szomszédos prímtől.
5; 53; 157; 173; 211; 257; 263; 373; 563; 593; 607; 653; 733; 947; 977; 1103; 1123; 1187; 1223; 1367; 1511; 1747; 1753; 1907; 2287; 2417; 2677; 2903; 2963; 3307; 3313; 3637; 3733 (A006562 sorozat az OEIS-ben)
Középpontos sokszögprímek
Prímek, melyek középpontos sokszögszámok.
Középpontos háromszögprímek
Prímek, melyek középpontos háromszögszámok.
Alakjuk: (3n2 + 3n + 2) / 2.
19; 31; 109; 199; 409; 571; 631; 829; 1489; 1999; 2341; 2971; 3529; 4621; 4789; 7039; 7669; 8779; 9721; 10459; 10711; 13681; 14851; 16069; 16381; 17659; 20011; 20359; 23251 (A125602 sorozat az OEIS-ben)
Középpontos négyszögprímek
Prímek, melyek középpontos négyszögszámok.
Alakjuk: .
5; 13; 41; 61; 113; 181; 313; 421; 613; 761; 1013; 1201; 1301; 1741; 1861; 2113; 2381; 2521; 3121; 3613; 4513; 5101; 7321; 8581; 9661; 9941; 10513; 12641; 13613; 14281; 14621 (A027862 sorozat az OEIS-ben)
Középpontos hatszögprímek
Prímek, melyek középpontos hatszögszámok.
Alakjuk: (7n2 ‒ 7n + 2) / 2.
43; 71; 197; 463; 547; 953; 1471; 1933; 2647; 2843; 3697; 4663; 5741; 8233; 9283; 10781; 11173; 12391; 14561; 18397; 20483; 29303; 29947; 34651; 37493; 41203; 46691 (A069099 sorozat az OEIS-ben)
Középpontos tízszögprímek
Prímek, melyek középpontos tízszögszámok.
Alakjuk: .
11; 31; 61; 101; 151; 211; 281; 661; 911; 1051; 1201; 1361; 1531; 1901; 2311; 2531; 3001; 3251; 3511; 4651; 5281; 6301; 6661; 7411; 9461; 9901; 12251; 13781; 14851; 15401; 18301; 18911; 19531 (A090562 sorozat az OEIS-ben)
Kubai prímek
Alakjuk: ; :
7; 19; 37; 61; 127; 271; 331; 397; 547; 631; 919; 1657; 1801; 1951; 2269; 2437; 2791; 3169; 3571; 4219; 4447; 5167; 5419; 6211; 7057; 7351; 8269; 9241; 10267; 11719; 12097; 13267; 13669 (A002407 sorozat az OEIS-ben)
Alakjuk:; :
13; 109; 193; 433; 769; 1201; 1453; 2029; 3469; 3889; 4801; 10093; 12289; 13873; 18253; 20173; 21169; 22189; 28813; 37633; 43201; 47629; 60493; 63949; 65713; 69313 (A002648 sorozat az OEIS-ben)
Kynea-prímek
![]() | Bővebben: Kynea-számok |
alakú prímek.
7; 23; 79; 1087; 66047; 263167; 16785407; 1073807359; 17180131327; 68720001023; 4398050705407; 70368760954879; 18014398777917439; 18446744082299486207 (A091514 sorozat az OEIS-ben)
Leyland-prímek
![]() | Bővebben: Leyland-prímek |
![]() | Bővebben: Leyland-számok |
Leyland-prímek az xy + yx alakban felírható prímek, ahol 1 < x ≤ y.
17; 593; 32993; 2097593; 8589935681; 59604644783353249; 523347633027360537213687137; 43143988327398957279342419750374600193 (A094133 sorozat az OEIS-ben)
Lucas-prímek
A Lucas-sorozat prím tagjai. A Lucas-sorozat definíciója:
L0 = 2; L1 = 1; Ln = Ln-1 + Ln-2.
Megoszlanak a vélemények arról, hogy az L0 = 2 beleszámít-e a Lucas-számok közé.
(2;) 3; 7; 11; 29; 47; 199; 521; 2207; 3571; 9349; 3010349; 54018521; 370248451; 6643838879; 119218851371; 5600748293801; 688846502588399; 32361122672259149 (A005479 sorozat az OEIS-ben)
Markov-prímek
Olyan p prímek, amelyekre létezik olyan x és y, amelyekkel .
2; 5; 13; 29; 89; 233; 433; 1597; 2897; 5741; 7561; 28657; 33461; 43261; 96557; 426389; 514229 (A002559 sorozat az OEIS-ben)
Mersenne-prímek
![]() | Bővebben: Mersenne-prímek |
A 2n ‒ 1 alakú prímszámok. Az első 12 Mersenne-prím:
3; 7; 31; 127; 8191; 131071; 524287; 2147483647; 2305843009213693951; 618970019642690137449562111; 162259276829213363391578010288127; 170141183460469231731687303715884105727 (A000668 sorozat az OEIS-ben)
A 13.-nak és a 14.-nek (tízes számrendszerben) 157 illetve 183 számjegye van.
2018 januárjában összesen 50 Mersenne-prím ismert. Az 50. Mersenne-prím a 277 232 917−1 szám, ez 23 249 425 számjeggyel írható fel a tízes számrendszerben.[6]
Mills-prímek
A alakú prímek, ahol θ a Mills-állandó. Ez a formula minden pozitív n-re prímszámot ad.
2; 11; 1361; 2521008887; 16022236204009818131831320183 (A051254 sorozat az OEIS-ben)
Mírpszámok
A mírpszámok („prím” visszafelé olvasva, angolul emirp) olyan prímek, melyeknek a decimális számjegyeit visszafelé olvasva is prímet kapunk, és nem palindrom prímek.
13; 17; 31; 37; 71; 73; 79; 97; 107; 113; 149; 157; 167; 179; 199; 311; 337; 347; 359; 389; 701; 709; 733; 739; 743; 751; 761; 769; 907; 937; 941; 953; 967; 971; 983; 991, 1009 (A006567 sorozat az OEIS-ben)
Motzkin-prímek
![]() | Bővebben: Motzkin-számok |
2; 127; 15511; 953467954114363 (A092832 sorozat az OEIS-ben)
Newman-Shanks-Williams-prímek
Olyan Newman-Shanks-Williams-számok, amelyek prímek.
7; 41; 239; 9369319; 63018038201; 489133282872437279; 19175002942688032928599 (A088165 sorozat az OEIS-ben)
Padovan-prímek
A Padovan-sorozat prím tagjai.
P(0) = P(1) = P(2) = 1; P(n) = P(n - 2)+P(n - 3)
2; 3; 5; 7; 37; 151; 3329; 23833; 13091204281; 3093215881333057; 1363005552434666078217421284621279933627102780881053358473 (A100891 sorozat az OEIS-ben)
Palindrom-prímek
![]() | Bővebben: Palindromszámok |
Olyan prímek, amelyeknek decimális számjegyei palindromát alkotnak, azaz balról jobbra és jobbról balra olvasva ugyanazt a számot adják:
2; 3; 5; 7; 11; 101; 131; 151; 181; 191; 313; 353; 373; 383; 727; 757; 787; 797; 919; 929; 10301; 10501; 10601; 11311; 11411; 12421; 12721; 12821; 13331; 13831; 13931; 14341; 14741 (A002385 sorozat az OEIS-ben)
Páros prímek
2n alakú prímszám csak egy van, a 2.
Páratlan prímek
Páratlan prímek, tehát a 2 kivételével minden prím.
Pell-prímek
A Pell-sorozat prím tagjai.
P0 = 0; P1 = 1; Pn = 2Pn-1 + Pn-2.
2; 5; 29; 5741; 33461; 44560482149; 1746860020068409; 68480406462161287469; 13558774610046711780701; 4125636888562548868221559797461449 (A086383 sorozat az OEIS-ben)
Permutálható prímek
Olyan prím, ahol a (tízes számrendszerben vett) számjegyek minden permutációja prímet ad.
2; 3; 5; 7; 11; 13; 17; 31; 37; 71; 73; 79; 97; 113; 131; 199; 311; 337; 373; 733; 919; 991; 1111111111111111111; 11111111111111111111111 (A003459 sorozat az OEIS-ben)
Sejtés, hogy minden további permutálható prím is csak 1-es számjegyekből áll.
Perrin-prímek
A Perrin-sorozat prím tagjai:
P(0) = 3; P(1) = 0; P(2) = 2; P(n) = P(n ‒ 2) + P(n ‒ 3)
2; 3; 5; 7; 17; 29; 277; 367; 853; 14197; 43721; 1442968193; 792606555396977; 187278659180417234321; 66241160488780141071579864797 (A074788 sorozat az OEIS-ben)
Pierpont-prímek
A alakú prímek u, v ≥ 0 egész számokra.
2; 3; 5; 7; 13; 17; 19; 37; 73; 97; 109; 163; 193; 257; 433; 487; 577; 769; 1153; 1297; 1459; 2593; 2917; 3457; 3889; 10369; 12289; 17497; 18433; 39367; 52489; 65537; 139969; 147457 (A005109 sorozat az OEIS-ben)
Pillai-prímek
![]() | Bővebben: Pillai-prímek |
23; 29; 59; 61; 67; 71; 79; 83; 109; 137; 139; 149; 193; 227; 233; 239; 251; 257; 269; 271; 277; 293; 307; 311; 317; 359; 379; 383; 389; 397; 401; 419; 431; 449; 461; 463; 467; 479; 499 (A063980 sorozat az OEIS-ben)
Pitagorasz-prímek
![]() | Bővebben: Pitagoraszi számok |
4n + 1 alakú prímek.
5; 13; 17; 29; 37; 41; 53; 61; 73; 89; 97; 101; 109; 113; 137; 149; 157; 173; 181; 193; 197; 229; 233; 241; 257; 269; 277; 281; 293; 313; 317; 337; 349; 353; 373; 389; 397; 401; 409; 421; 433; 449 (A002144 sorozat az OEIS-ben)
Ezen prímek felírhatók 2 négyzetszám összegeként.
Prím-n-esek
Prímhármasok
(p; p+2; p+6) vagy (p; p+4; p+6) rendezett hármasok, ahol mind a három szám prím.
(5; 7; 11); (7; 11; 13); (11; 13; 17); (13; 17; 19); (17; 19; 23); (37; 41; 43); (41; 43; 47); (67; 71; 73); (97; 101; 103); (101; 103; 107); (103; 107; 109); (107; 109; 113); (191; 193; 197); (193; 197; 199); (223; 227; 229); (227; 229; 233); (277; 281; 283); (307; 311; 313); (311; 313; 317); (347; 349; 353) ((A007529 sorozat az OEIS-ben); (A098414 sorozat az OEIS-ben); (A098415 sorozat az OEIS-ben))
Prímnégyesek
(p; p+2; p+6; p+8) rendezett négyesek, ahol mind a négy szám prím.
(5; 7; 11; 13); (11; 13; 17; 19); (101; 103; 107; 109); (191; 193; 197; 199); (821; 823; 827; 829); (1481; 1483; 1487; 1489); (1871; 1873; 1877; 1879); (2081; 2083; 2087; 2089); (3251; 3253; 3257; 3259); (3461; 3463; 3467; 3469); (5651; 5653; 5657; 5659); (9431; 9433; 9437; 9439) ((A007530 sorozat az OEIS-ben); (A136720 sorozat az OEIS-ben); (A136721 sorozat az OEIS-ben); (A090258 sorozat az OEIS-ben))
Proth-prímek
![]() | Bővebben: Proth-számok |
k · 2n + 1 alakú prímek, ahol k páratlan és k < 2n
3; 5; 13; 17; 41; 97; 113; 193; 241; 257; 353; 449; 577; 641; 673; 769; 929; 1153; 1217; 1409; 1601; 2113; 2689; 2753; 3137; 3329; 3457; 4481; 4993; 6529; 7297; 7681; 7937; 9473; 9601; 9857 (A080076 sorozat az OEIS-ben)
Ramanujan-számok
Adott n számra a Ramanujan-szám (Rn) a legkisebb olyan szám, amelyre legalább n prím található az x/2 és x számok között minden x ≥ Rn számra.
2; 11; 17; 29; 41; 47; 59; 67; 71; 97; 101; 107; 127; 149; 151; 167; 179; 181; 227; 229; 233; 239; 241; 263; 269; 281; 307; 311; 347; 349; 367; 373; 401; 409; 419; 431; 433; 439; 461; 487; 491 (A104272 sorozat az OEIS-ben)
Repunit-prímek
![]() | Bővebben: Repunit |
Olyan prímek, amelyek (tízes számrendszerben) csak az 1-es számjegyet tartalmazzák.
11; 1111111111111111111; 11111111111111111111111 (A004022 sorozat az OEIS-ben)
A következőnek 317, az azt követőnek pedig 1031 számjegye van.
Smarandache-Wellin-prímek
Az első n prímszám decimális reprezentációjának (leírásának) konkatenációjával (egymás után fűzésével) keletkező prím.
2; 23; 2357 (A069151 sorozat az OEIS-ben)
A negyedik Smarandache-Wellin-prím az első 128 prímszám konkatenációja, így 719-re végződik.
Sophie Germain-prímek
![]() | Bővebben: Sophie Germain-prímek |
Ahol p és 2p + 1 egyaránt prím.
2; 3; 5; 11; 23; 29; 41; 53; 83; 89; 113; 131; 173; 179; 191; 233; 239; 251; 281; 293; 359; 419; 431; 443; 491; 509; 593; 641; 653; 659; 683; 719; 743; 761; 809; 911; 953 (A005384 sorozat az OEIS-ben)
Stern-prímek
Olyan prímek, amelyek nem állnak elő egy kisebb prím és egy négyzetszám kétszeresének összegeként.
2; 3; 17; 137; 227; 977; 1187; 1493 (A042978 sorozat az OEIS-ben)
2008 januárjában csak ezek a Stern-prímek ismertek.
Szexi prímek
Olyan prímek, ahol p és p + 6 egyaránt prímek. Az elnevezés a latin sex szóból származik, ami 6-ot jelent.
(5,11); (7,13); (11,17); (13,19); (17,23); (23,29); (31,37); (37,43); (41,47); (47,53); (53,59); (61,67); (67,73); (73,79); (83,89); (97,103); (101,107); (103,109); (107,113); (131,137); (151,157); (157,163); (167,173); (173,179); (191,197); (193,199) (A023201 sorozat az OEIS-ben); (A046117 sorozat az OEIS-ben)
Szuper prímek
Olyan prímek, amelyeknek a prímszámok sorozatában vett indexe is prímszám. Tehát például a 2., a 3., az 5. prímszám.
3; 5; 11; 17; 31; 41; 59; 67; 83; 109; 127; 157; 179; 191; 211; 241; 277; 283; 331; 353; 367; 401; 431; 461; 509; 547; 563; 587; 599; 617; 709; 739; 773; 797; 859; 877; 919; 967; 991 (A006450 sorozat az OEIS-ben)
Szuperszinguláris prímek
Pontosan 15 darab szuperszinguláris prímről tudunk.
2; 3; 5; 7; 11; 13; 17; 19; 23; 29; 31; 41; 47; 59; 71 (A002267 sorozat az OEIS-ben)
Szimmetrikus prímek
Definíció:
Egy prímszám (tízes számrendszerben) szimmetrikus prím, ha:
- a) minden számjegye prím,
- b) számjegyeinek száma prím,
- c) számjegyeinek összege prím,
- d) a szám középpontosan szimmetrikus a középső számjegyre.
353, 373, 757, 32323, 33533, 35353, 35753, 75557, 77377 stb.
International Organisation of Scientific Research: "Symmetrical Prime Numbers" 2019-01–20
https://web.archive.org/web/20170613172808/http://iosrjournals.org/iosr-jpte/pages/v6-i1.html
Teljes prímek
Definíció:
Egy prímszám (tízes számrendszerben) teljes prím, ha:
- a) minden számjegye prím,
- b) számjegyeinek száma is prím.
23, 37, 53, 73,
223, 227, 233, 257, 277, 337, 353, 373, 523, 557, 577, 727, 733, 757, 773 stb.
Bölcsföldi-Birkás-Ferenczi prime numbers (Full prime numbers)
International Journal of Mathematics and Statistics Invention:
http://www.ijmsi.org/Papers/Volume.5.Issue.2/B05020407.pdf
és ELTE, ANNALES ... COMPUTATORICA, évkönyv, 2015 pp 221–226: VOLLPRIMZAHLENMENGE
Thabit-prímek
![]() | Bővebben: Thabit-prímek |
3 · 2n - 1 alakú prímszámok.
2; 5; 11; 23; 47; 191; 383; 6143; 786431; 51539607551; 824633720831; 26388279066623; 108086391056891903; 55340232221128654847; 226673591177742970257407 (A007505 sorozat az OEIS-ben)
Többrészes prímek
Definíció:
Négyrészes prímek:
Egy prímszám (tízes számrendszerben) négyrészes prím, ha:
- a) a számjegyek száma 4k, ahol k ≥ 1 egész,
- b) négy egyenlő hosszú részre osztva a számot, mindegyik rész is prím.
2237, 2273, 2333, 2357, 2377, 2557, 2777 stb.
Ugyanígy értelmezhetők az ötrészes, hatrészes, n-részes prímek.
http://www.ijlera.com/current-issue.html
Bölcsföldi-Birkás-Ács-Bereznainé Sepetyuk Nóra-Szegedi Marcell:
"More parts prime numbers"
Ulam-prímek
Olyan Ulam-számok, amelyek prímek.
2; 3; 11; 13; 47; 53; 97; 131; 197; 241; 409; 431; 607; 673; 739; 751; 983; 991; 1103; 1433; 1489; 1531; 1553; 1709; 1721; 2371; 2393; 2447; 2633; 2789; 2833; 2897 (A068820 sorozat az OEIS-ben)
Unokatestvér prímek
Olyan prímszám-párok, amelyek különbsége 4.
(p; p + 4) alakú prímszám párok.
(3; 7; 11); (13; 17); (19; 23); (37; 41); (43; 47); (67; 71); (79; 83); (97; 101); (103; 107); (109; 113); (127; 131); (163; 167); (193; 197); (223; 227); (229; 233); (277; 281) (A023200 sorozat az OEIS-ben); (A046132 sorozat az OEIS-ben)
Wagstaff-prímek
![]() | Bővebben: Wagstaff-prímek |
(2n + 1) / 3 alakú prímszámok.
3; 11; 43; 683; 2731; 43691; 174763; 2796203; 715827883; 2932031007403; 768614336404564651; 201487636602438195784363; 845100400152152934331135470251; 56713727820156410577229101238628035243 (A000979 sorozat az OEIS-ben)
A hozzájuk tartozó n értékek a következők:
3; 5; 7; 11; 13; 17; 19; 23; 31; 43; 61; 79; 101; 127; 167; 191; 199; 313; 347; 701; 1709; 2617; 3539; 5807; 10501; 10691; 11279; 12391; 14479; 42737; 83339; 95369; 117239; 127031; 138937; 141079; 267017; 269987; 374321 (A000978 sorozat az OEIS-ben)
Wedderburn-Etherington-prímek
Olyan Wedderburn-Etherington-számok, amelyek prímek.
2; 3; 11; 23; 983; 2179; 24631; 3626149; 253450711; 596572387 (A001190 sorozat az OEIS-ben)
Wieferich-prímek
![]() | Bővebben: Wieferich-prímek |
Olyan prímek, amelyekre p2 osztja a 2p ‒ 1 ‒ 1 számot.
1093; 3511 (A001220 sorozat az OEIS-ben)
2016 decemberében csak ezek a Wieferich-prímek ismertek.
Wilson-prímek
Olyan p prímszámok, amelyekre p2 osztja a (p ‒ 1)! + 1 számot.
5; 13; 563 (A007540 sorozat az OEIS-ben)
2008 januárjában csak ezek a Wilson-prímek ismertek.
Wolstenholme-prímek
![]() | Bővebben: Wolstenholme-számok |
Olyan p prímek, amelyekre fennáll az alábbi kongruencia:
.
16843; 2124679 (A088164 sorozat az OEIS-ben)
2008 januárjában csak ezek a Wolstenholme-prímek ismertek.
Woodall-prímek
![]() | Bővebben: Woodall-számok |
n · 2n ‒ 1 alakú prímszámok.
7; 23; 383; 32212254719; 2833419889721787128217599; 195845982777569926302400511; 4776913109852041418248056622882488319 (A050918 sorozat az OEIS-ben)
Jegyzetek
- ↑ (A046704 sorozat az OEIS-ben)
- ↑ Bölcsföldi József–BirkásGyörgy (2017. 12). „Golden ratio prime numbers” (angol nyelven) (PDF). International Journal of Engineering Science Invention 6 (12), 82-85. o. ISSN 2319–6726.
- ↑ Bölcsföldi József – Birkás György: IOSR Journal of Mathematics: Bölcsföldi-Birkás Prime Numbers. iosrjournals.org (angolul) (2017) (Hozzáférés: 2017. június 13.) (pdf)
- ↑ International Journal of Engineering and Science Invention: Bölcsföldi-Dömötör prime numbers, 13-12-2018
- ↑ (A064152 sorozat az OEIS-ben)
- ↑ List of Known Mersenne Prime Numbers. mersenne.org. (Hozzáférés: 2018. január 3.)
Források
- Prímlista
- Interfész 98 millió prímszámhoz (A 8 milliárdnál kisebb prímszámok.)
- az első 130 millió prímszám
- Weisstein, Eric W.: Prime Number Sequences (angol nyelven). Wolfram MathWorld
- Prímekkel kapcsolatos sorozatok (On-Line Encyclopedia of Integer Sequences, röviden OEIS).
Matematikaportál • összefoglaló, színes tartalomajánló lap