151212(2)

Ruby


Chebyshev's bias(2)

もう少し調べてみた。

require 'prime'

def f(n)
  ary = []
  cnt1, cnt2, cnt3 = 0, 0, 0
  # cnt1 > cnt3 となることは滅多にないのでたくさんの素数を用意
  Prime.each(n).each{|i|
    if i > 2
      i % 4 == 1? cnt1 += 1 : cnt3 += 1
    else
      cnt2 += 1
    end
    ary << i if cnt1 > cnt3
  }
  ary
end

p f(5 * 10 ** 8)

出力結果
[26861, 616841, 616849, 616877, 616897, 616909, 616933, 616943, 616951, 616961, 616991, 616997, 616999, 617011, 617269, 617273, 617293, 617311, 617327, 617333, 617339, 617341, 617359, 617369, 617401, 617429, 617453, 617521, 617537, 617689, 617693, 617699, 617717, 622813, 622849, 622861, 622879, 622889, 622901, 622927, 622943, 622957, 622967, 622987, 622997, 623003, 623009, 623017, 623023, 623041, 623057, 623059, 623071, 623107, 623209, 623221, 623261, 623263, 623269, 623279, 623281, 623291, 623299, 623321, 623341, 623353, 623401, 623417, 623423, 623437, 623477, 623521, 623531, 623537, 623563, 623591, 623617, 623621, 623633, 623641, 623653, 623669, 623671, 623677, 623681, 623683, 623699, 623717, 623719, 623723, 623729, 623743, 623759, 623767, 623771, 623803, 623933, 623957, 623977, 623989, 624097, 624133, 624149, 624241, 626929, 626953, 627353, 627377, 627379, 627449, 627481, 627733, 627749, 627773, 627787, 627791, 627797, 627799, 627841, 627901, 628013, 628021, 628037, 628049, 628051, 628057, 628063, 628093, 628097, 628127, 628139, 628171, 628183, 628189, 628193, 628207, 628213, 628217, 628219, 628231, 628261, 628267, 628289, 628301, 628319, 628357, 628363, 628373, 628379, 628391, 628399, 628937, 628973, 628993, 628997, 629003, 629009, 629011, 629023, 629029, 629059, 629081, 629113, 629137, 629143, 629171, 629177, 629203, 629243, 629249, 629263, 629281, 629311, 629341, 629429, 629449, 629467, 629513, 629537, 629567, 629569, 629591, 629593, 629609, 629611, 629617, 629623, 629653, 629683, 629687, 629689, 629701, 629711, 629723, 629737, 629743, 630737, 630797, 630803, 632813, 632897, 633013, 633037, 633053, 633067, 633079, 633133, 633161, 633197, 633209, 633221, 633253, 633257, 633263, 633271, 633287, 633307, 633317, 633337, 633359, 633377, 633379, 633383, 633401, 633407, 633449, 633461, 633463, 633469, 633473, 633487, 633497, 633559, 633569, 633571, 633649, 633653, 633667, 633797, 12306137, 12306149, 12306157, 12306187, 12306193, 12306197, 12306211, 12306223, 12306241, 12306253, 12306269, 12306277, 12306313, 12306331, 12306341, 12306367, 12306373, 12306379, 12306407, 12306409, 12306421, 12306431, 12306439, 12306443, 12306457, 12306461, 12306467, 12306479, 12306517, 12308113, 12308117, 12308123, 12308141, 12308173, 12308201, 12308207, 12308227, 12308237, 12308249, 12308269, 12308297, 12308327, 12308339, 12308353, 12308393, 12308399, 12308411, 12308419, 12308423, 12308453, 12308467, 12308507, 12308509, 12308539, 12308573, 12309893, 12309961, 12310013, 12310019, 12310021, 12310027, 12310033, 12310073, 12310079, 12310093, 12310097, 12310121, 12310147, 12310153, 12310163, 12310187, 12310219, 12310229, 12310253, 12310279, 12310289, 12310301, 12310303, 12310321, 12310327, 12310357, 12310369, 12310387, 12310411, 12310421, 12310429, 12310439, 12310447, 12310453, 12310481, 12310489, 12310511, 12310531, 12310541, 12310547, 12310549, 12310591, 12310607, 12310609, 12310621, 12310637, 12310657, 12310667, 12310679, 12310687, 12310699, 12310721, 12310733, 12310741, 12310759, 12310801, 12310817, 12310847, 12310849, 12310861, 12310867, 12310871, 12310889, 12310913, 12310927, 12310931, 12310933, 12310951, 12310967, 12310979, 12310997, 12311017, 12311023, 12311027, 12311053, 12311059, 12311063, 12311087, 12311093, 12311113, 12311119, 12311137, 12311147, 12311149, 12311153, 12311191, 12311207, 12311209, 12311219, 12311251, 12311261, 12311267, 12311333, 12311401, 12311657, 12311837, 12311869, 12311881, 12311911, 12311917, 12311933, 12311939, 12311951, 12311977, 12311983, 12311989, 12312011, 12312017, 12312023, 12312197, 12312217, 12312221, 12312227, 12312241, 12312263, 12312277, 12312281, 12312283, 12312331, 12312347, 12312353, 12312359, 12312397, 12312401, 12312407, 12312413, 12312427, 12312431, 12312457, 12312497, 12312557, 12312581, 12312661, 12312689, 12312701, 12312719, 12312737, 12312763, 12313309, 12313333, 12313337, 12313339, 12313361, 12313363, 12313369, 12313381, 12313393, 12313409, 12313447, 12313451, 12313513, 12313537, 12313549, 12313573, 12313591, 12313619, 12313633, 12313657, 12313663, 12313669, 12313673, 12313703, 12313709, 12313747, 12313751, 12313759, 12313783, 12313787, 12313799, 12313801, 12313813, 12313877, 12313907, 12313909, 12313927, 12313937, 12313999, 12314011, 12314023, 12314051, 12314321, 12314333, 12314353, 12314363, 12314369, 12314381, 12314417, 12314429, 12314431, 12314459, 12314479, 12314483, 12314509, 12314513, 12314537, 12314563, 12314569, 12314587, 12314597, 12314629, 12314633, 12314639, 12314651, 12314677, 12314689, 12314699, 12314767, 12314773, 12314789, 12314791, 12314803, 12314807, 12314837, 12314839, 12314873, 12314891, 12314903, 12314909, 12314941, 12314947, 12314971, 12314993, 12315001, 12315013, 12315077, 12315101, 12315103, 12315109, 12315113, 12315131, 12315161, 12315187, 12315209, 12315223, 12315241, 12315253, 12315271, 12315283, 12315299, 12315301, 12315323, 12315349, 12315353, 12315367, 12315371, 12315383, 12315403, 12315427, 12315449, 12315461, 12315467, 12315469, 12315481, 12315493, 12315509, 12315521, 12315529, 12315559, 12315577, 12315581, 12315613, 12315617, 12315631, 12315643, 12315647, 12315659, 12315661, 12315671, 12315679, 12315707, 12315713, 12315727, 12315811, 12315829, 12315841, 12315851, 12315881, 12315883, 12315929, 12315943, 12315967, 12315991, 12316033, 12316037, 12316061, 12316081, 12316091, 12316093, 12316111, 12316133, 12316151, 12316159, 12316169, 12316181, 12316219, 12316223, 12316229, 12316231, 12316259, 12316267, 12316289, 12316321, 12316349, 12316357, 12316391, 12316399, 12316411, 12316429, 12316433, 12316439, 12316457, 12316471, 12316529, 12316531, 12316547, 12316589, 12316609, 12316627, 12316631, 12316639, 12316643, 12316691, 12316697, 12316699, 12316709, 12316727, 12316741, 12316747, 12316783, 12316813, 12316831, 12316853, 12316861, 12316873, 12316879, 12316901, 12316903, 12316949, 12316957, 12316979, 12317177, 12317209, 12317233, 12317251, 12317273, 12317281, 12317287, 12317297, 12317309, 12317311, 12317317, 12317321, 12317329, 12317341, 12317353, 12317381, 12317407, 12317423, 12317441, 12317467, 12317471, 12317483, 12317497, 12317531, 12317563, 12317573, 12317587, 12317597, 12317623, 12317647, 12317693, 12317729, 12317743, 12317771, 12317797, 12317803, 12317813, 12317827, 12317831, 12317863, 12317869, 12317897, 12317923, 12317927, 12317939, 12317941, 12317957, 12317971, 12317983, 12317989, 12317993, 12318043, 12318071, 12318221, 12319753, 12319777, 12319793, 12321149, 12321161, 12322001, 12322217, 12322237, 12322301, 12322309, 12322333, 12322337, 12322351, 12322391, 12322397, 12322421, 12322423, 12322451, 12322523, 12322529, 12322543, 12322577, 12322579, 12322613, 12322631, 12322649, 12323357, 12323693, 12323713, 12323737, 12323777, 12323783, 12323789, 12323797, 12323807, 12323809, 12323813, 12323851, 12323863, 12323887, 12323897, 12323911, 12323977, 12323981, 12323999, 12324041, 12324077, 12324107, 12324127, 12324139, 12324161, 12324163, 12324203, 12324209, 12324211, 12324229, 12324233, 12324239, 12324253, 12324271, 12324353, 12324409, 12324413, 12324419, 12324437, 12324497, 12324607, 12324629, 12324647, 12324659, 12324679, 12324769, 12324821, 12325057, 12325069, 12325081, 12325099, 12325121, 12325123, 12325141, 12327857, 12327881, 12327883, 12327901, 12327949, 12328037, 12328181, 12328189, 12328223, 12332989, 12332993, 12333001, 12333017, 12333019, 12333031, 12333043, 12333073, 12333089, 12333103, 12333107, 12333157, 12334841, 12334873, 12334897, 12334909, 12334913, 12334919, 12334939, 12334943, 12335093, 12350017, 12350033, 12350053, 12350069, 12350081, 12350083, 12350087, 12350089, 12350099, 12350141, 12350153, 12350161, 12350197, 12350203, 12350207, 12350249, 12350281, 12350309, 12350321, 12350339, 12350353, 12350357, 12350363, 12350383, 12350407, 12350419, 12350423, 12350453, 12350467, 12350479, 12350497, 12350501, 12350509, 12350543, 12350581, 12350641, 12350659, 12350671, 12350683, 12350693, 12350699, 12350773, 12350777, 12350783, 12350827, 12350837, 12350851, 12350861, 12350867, 12350873, 12350879, 12350887, 12350911, 12350929, 12350941, 12350951, 12350953, 12350971, 12350983, 12351011, 12351029, 12351041, 12351047, 12351049, 12351103, 12351133, 12351193, 12351203, 12351217, 12351221, 12351223, 12351233, 12351247, 12351263, 12351289, 12351319, 12351323, 12351329, 12351343, 12351359, 12351371, 12360421, 12360449, 12360457, 12360473, 12360497, 12360503, 12360527, 12360539, 12360541, 12360563, 12360611, 12360617, 12360619, 12360889, 12360937, 12360949, 12360977, 12361003, 12361007, 12361009, 12361021, 12361061, 12361067, 12361073, 12361093, 12361103, 12361177, 12361187, 12361199, 12361201, 12361211, 12361241, 12361249, 12361277, 12361303, 12361351, 12361379, 12361399, 12361403, 12361417, 12361429, 12361451, 12361513, 12361537, 12361543, 12361549, 12361577, 12361607, 12361619, 12361673, 12361729, 12361733, 12361753, 12361759, 12361793, 12361807, 12361813, 12361819, 12361829, 12361831, 12361847, 12361849, 12361871, 12361883, 12361889, 12361891, 12361897, 12361903, 12361933, 12361949, 12361961, 12361997, 12362003, 12362029, 12362041, 12362057, 12362059, 12362069, 12362071, 12362089, 12362099, 12362117, 12362123, 12362131, 12362143, 12362153, 12362159, 12362167, 12362173, 12362177, 12362209, 12362221, 12362227, 12362249, 12362257, 12362261, 12362263, 12362291, 12362297, 12362309, 12362327, 12362333, 12362347, 12362351, 12362353, 12362387, 12362393, 12362401, 12362411, 12362419, 12362423, 12362437, 12362461, 12362479, 12362489, 12362513, 12362531, 12362533, 12362557, 12362573, 12362593, 12362599, 12362611, 12362617, 12362633, 12362641, 12362653, 12362657, 12362659, 12362677, 12362717, 12362719, 12362737, 12362741, 12362759, 12362783, 12362797, 12362803, 12362827, 12362837, 12362839, 12362849, 12362851, 12362873, 12362879, 12362881, 12362899, 12362929, 12362951, 12362953, 12362957, 12362969, 12362981, 12362989, 12363007, 12363011, 12363031, 12363047, 12363049, 12363067, 12363083, 12363089, 12363133, 12363137, 12363139, 12363149, 12363161, 12363173, 12363179, 12363223, 12363227, 12363229, 12363271, 12363283, 12363311, 12363313, 12363331, 12363347, 12363349, 12363361, 12363371, 12363383, 12363401, 12363409, 12363413, 12363467, 12363479, 12363493, 12363497, 12363517, 12363521, 12363551, 12363569, 12363583, 12363629, 12363643, 12363647, 12363653, 12363667, 12363677, 12363691, 12363707, 12363731, 12363733, 12363739, 12363749, 12363751, 12363803, 12363817, 12363821, 12363829, 12363847, 12363859, 12363881, 12363887, 12363931, 12363941, 12363943, 12363973, 12363991, 12363997, 12364007, 12364019, 12364021, 12364057, 12364103, 12364111, 12364123, 12364129, 12364141, 12364181, 12364199, 12364213, 12364259, 12364267, 12364279, 12364283, 12364351, 12364357, 12364361, 12364367, 12364379, 12364393, 12364399, 12364403, 12364433, 12364441, 12364487, 12364489, 12364507, 12364537, 12364543, 12364591, 12364601, 12364603, 12364609, 12364613, 12364621, 12364637, 12364663, 12364669, 12364673, 12364699, 12364711, 12364717, 12364727, 12364733, 12364747, 12364757, 12364769, 12364789, 12364819, 12364837, 12364861, 12364879, 12364889, 12364897, 12364907, 12364909, 12364921, 12364927, 12364943, 12364949, 12364973, 12364981, 12364997, 12364999, 12365009, 12365033, 12365057, 12365071, 12365083, 12365113, 12365117, 12365153, 12365173, 12365179, 12365189, 12365201, 12365203, 12365207, 12365261, 12365291, 12365293, 12365303, 12365321, 12365347, 12365351, 12365369, 12365383, 12365389, 12365399, 12365407, 12365411, 12365413, 12365429, 12365449, 12365461, 12365473, 12365491, 12365501, 12365503, 12365519, 12365539, 12365567, 12365569, 12365581, 12365593, 12365597, 12365603, 12365611, 12365623, 12365627, 12365663, 12365677, 12365701, 12365711, 12365729, 12365741, 12365767, 12365777, 12365779, 12365797, 12365813, 12365819, 12365831, 12365833, 12365839, 12365891, 12365893, 12365911, 12365917, 12365923, 12365933, 12365939, 12365959, 12366023, 12366037, 12366041, 12366061, 12366071, 12366073, 12366083, 12366091, 12366113, 12366121, 12366139, 12366163, 12366173, 12366181, 12366187, 12366197, 12366247, 12366271, 12366287, 12366301, 12366337, 12366353, 12366401, 12366407, 12366421, 12366449, 12366451, 12366467, 12366493, 12366503, 12366509, 12366521, 12366527, 12366533, 12366569, 12366589, 12366619, 12366623, 12366631, 12366637, 12366643, 12366703, 12366721, 12366763, 12366779, 12366787, 12366791, 12366797, 12366811, 12366839, 12366859, 12366863, 12366869, 12366883, 12366899, 12366919, 12366961, 12366971, 12366979, 12366989, 12367027, 12367037, 12367039, 12367057, 12367067, 12367099, 12367111, 12367129, 12367141, 12367151, 12367163, 12367181, 12367189, 12367207, 12367259, 12367291, 12367297, 12367321, 12367331, 12367337, 12367339, 12367409, 12367417, 12367451, 12367457, 12367471, 12367489, 12367493, 12367501, 12367507, 12367559, 12367571, 12367573, 12367577, 12367591, 12367631, 12367637, 12367643, 12367669, 12367673, 12367679, 12367681, 12367697, 12367711, 12367723, 12367739, 12367759, 12367763, 12367769, 12367781, 12367783, 12367787, 12367793, 12367807, 12367819, 12367829, 12367837, 12367847, 12367867, 12367871, 12367877, 12367889, 12367897, 12367919, 12367967, 12367969, 12367973, 12367981, 12367991, 12368009, 12368017, 12368021, 12368029, 12368051, 12368053, 12368071, 12368087, 12368093, 12368099, 12368131, 12368143, 12368173, 12368203, 12368207, 12368233, 12368243, 12368269, 12368281, 12368309, 12368311, 12368329, 12368357, 12368381, 12368387, 12368393, 12368399, 12368417, 12368423, 12368437, 12368441, 12368443, 12368453, 12368459, 12368467, 12368479, 12368491, 12368507, 12368509, 12368513, 12368539, 12368579, 12368581, 12368591, 12368599, 12368621, 12368633, 12368651, 12368683, 12368689, 12368717, 12368729, 12368789, 12368813, 12368831, 12368833, 12368857, 12368861, 12368869, 12368887, 12368891, 12368893, 12368899, 12368903, 12368927, 12368933, 12368947, 12368971, 12369011, 12369017, 12369041, 12369043, 12369059, 12369073, 12369083, 12369103, 12369107, 12369113, 12369121, 12369127, 12369143, 12369157, 12369163, 12369169, 12369179, 12369187, 12369197, 12369199, 12369221, 12369223, 12369233, 12369257, 12369263, 12369277, 12369281, 12369317, 12369347, 12369349, 12369367, 12369443, 12369449, 12369451, 12369463, 12369479, 12369499, 12369503, 12369529, 12369541, 12369547, 12369613, 12369629, 12369671, 12369677, 12369719, 12369757, 12369781, 12369787, 12369809, 12369821, 12369839, 12369859, 12369869, 12369871, 12369887, 12369919, 12369941, 12369943, 12369953, 12369967, 12370003, 12370031, 12370049, 12370051, 12370079, 12370087, 12370091, 12370093, 12370109, 12370157, 12370201, 12370219, 12370229, 12370249, 12370307, 12370331, 12370357, 12370367, 12370381, 12370409, 12370429, 12370433, 12370439, 12370451, 12370483, 12370487, 12370499, 12370529, 12370549, 12370597, 12370601, 12370607, 12370621, 12370637, 12370639, 12370649, 12370651, 12370667, 12370681, 12370693, 12370697, 12370703, 12370717, 12370727, 12370741, 12370759, 12370763, 12370769, 12370777, 12370789, 12370801, 12370811, 12370837, 12370867, 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