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Topic: Perrin pseudoprimes to 10^13
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Rob

Posts: 2
Registered: 5/8/12
Perrin pseudoprimes to 10^13
Posted: Aug 22, 2012 8:45 AM
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Note some not square-free:

271441 = 521^2
16532714 = 2 * 11^2 * 53 * 1289
27422714 = 2 * 11^2 * 47 * 2411
36366108601 = 190699^2
96423785065 = 5 * 37 * 47 * 223^3
742355975834 = 2 * 11^2 * 1453^3
6401137442161 = 7 * 11 * 37 * 47 * 223 * 463^2

List below.

271441, 904631, 16532714, 24658561, 27422714, 27664033, 46672291,
102690901, 130944133, 196075949, 214038533, 517697641, 545670533,
801123451, 855073301, 903136901, 970355431, 1091327579, 1133818561,
1235188597, 1389675541, 1502682721, 2059739221, 2304156469,
2976407809, 3273820903, 3841324339, 3924969689, 4982970241,
5130186571, 5242624003, 6335800411, 7045248121, 7279379941,
7293442133, 7825642579, 8118449281, 8236954057, 8462866081,
8818340833, 8923398485, 9085378147, 10563944161, 11025178067,
11821223041, 12883213201, 13310695501, 13677931541, 13955714701,
14696080261, 14735895301, 15391036351, 16283099827, 17044925633,
17105582341, 18301178501, 18321066191, 19267579361, 19282969441,
19862784913, 20913703903, 22712568341, 23642383309, 24306384961,
24918616339, 26448696913, 27811217611, 28427760433, 30713796101,
30776966533, 32913078661, 33209126521, 33936030647, 33996510721,
36056194453, 36366108601, 37874758241, 39283248493, 39675460001,
40878145621, 43234580143, 43522383061, 46353274003, 46690026571,
46713465109, 47529840403, 47813279821, 50222978051, 52437986833,
53221978153, 55779259271, 56579408617, 59775613633, 60518537641,
61244006479, 61432660981, 65085388961, 67167538903, 67505599751,
69423917141, 70926396661, 71729181001, 74961121327, 77187046421,
79326686741, 80829302401, 83649293731, 84441389581, 86877918493,
88728966659, 90658522333, 92897571551, 93043273753, 96423785065,
97032879991, 97142408533, 101360093927, 104638639841, 108390509047,
116948450561, 118805562613, 120468146041, 121458570193, 126193928033,
126380942881, 126611608537, 126962978081, 132992584453, 133630799851,
135974972033, 138538741771, 141115654681, 141231910177, 142989300893,
144377609419, 147123850721, 147594411361, 147594592133, 149626359977,
165321688501, 167385219121, 167848253497, 168949933517, 177018088997,
181158720577, 182673406579, 197816411521, 198083076757, 204053282413,
215498833117, 217194446701, 217616635867, 222037960321, 224253349261,
227998977133, 228367064297, 231446297633, 232270782787, 236820060181,
237984673921, 240342960161, 254302215553, 257006991361, 259537439733,
260871285403, 263449230557, 269321227141, 275195556641, 277022954303,
277717986979, 278970089861, 283688430341, 291670228081, 298444756843,
299573056021, 303107033503, 305391469633, 307640704757, 315786049661,
316283776033, 318214733077, 320454854021, 323757774341, 362963502091,
364519238203, 364573433665, 372312582139, 374092582091, 374338731691,
386859866401, 397306276529, 397974452741, 398608452481, 405580454533,
407800554241, 415795447441, 434646492367, 440183439701, 440239216777,
440366619001, 440574238081, 453927271951, 461792694061, 463119872491,
466692573887, 468792594821, 475957681291, 479142783061, 479309924761,
480592182533, 490181014439, 503221305721, 525970243261, 534943933609,
535899751003, 540792078737, 543235514977, 549025745329, 550710084401,
554319945121, 564032917951, 566294280581, 567088537753, 573299215807,
574216398491, 575687567521, 588909469501, 597531432961, 599330239201,
607292642881, 617284316881, 626274657601, 637204302649, 642449097811,
642775534721, 644632798151, 652270080001, 660903938581, 679247007781,
679540558457, 680217818941, 683247332657, 686865696161, 692273696641,
706122938809, 717465754513, 721024720609, 721113629633, 726684442903,
740609610931, 741036895307, 742355975834, 743613653333, 749501156953,
761794523821, 770650220033, 772857772301, 773992007249, 776299741561,
786882624533, 790931685781, 791415668143, 792392692033, 800796067741,
803420820001, 809985734741, 814499623279, 821518204033, 860479802731,
867351820147, 876215372033, 876738156901, 882230073061, 888594405557,
897947322697, 909843653377, 917396032261, 936825893137, 951059771551,
953378194231, 961534093313, 962065853773, 971086573687, 981115040641,
989987687851, 1002207301651, 1003991970061, 1015985768533,
1018615209611, 1035126675703, 1047795720533, 1058765851609,
1063968734977, 1070780513617, 1071798984367, 1082242763141,
1083532984631, 1104433480957, 1109003521753, 1117652286871,
1136553093551, 1148851346653, 1166371476821, 1177211715841,
1202207315653, 1205634501841, 1223355803521, 1229715793153,
1230561460409, 1240088072653, 1241167603681, 1255657515001,
1260330659197, 1278007493041, 1301027497391, 1308751688161,
1309932915461, 1318733520133, 1321973632481, 1334379206161,
1338354050881, 1343891820451, 1369839382003, 1390006219717,
1390395117701, 1401584327821, 1402938605089, 1419399110533,
1425656109641, 1427897068421, 1432165575961, 1467576915121,
1475636192161, 1494760194181, 1494846933301, 1505059920781,
1542312888341, 1551498525061, 1555133400713, 1557142163011,
1565224100833, 1579210364033, 1583889182741, 1607735600551,
1633748373001, 1662888398341, 1675836511903, 1691708863441,
1699584557921, 1741047975703, 1757545322653, 1775593696069,
1790351308789, 1796441360617, 1796469560033, 1821259319529,
1845840831997, 1874180672033, 1888000349047, 1907646496003,
1920819287381, 1921741182593, 1931429039299, 1933211595421,
1940561518897, 1994390128901, 2003892101461, 2015395173881,
2032740937921, 2057839740547, 2063145131407, 2076246691817,
2076685312021, 2094986249441, 2103877896121, 2134462084453,
2139101704231, 2143595898181, 2152302898747, 2198992165921,
2205939950479, 2207973656387, 2209474705169, 2215923034573,
2240764981547, 2246266882133, 2248651614317, 2272553657409,
2277740968903, 2296700003333, 2314162406533, 2339928887381,
2344424576341, 2360359358281, 2449157208961, 2503654001551,
2579993418241, 2586691299349, 2593829758417, 2603117374903,
2609041763333, 2615037683473, 2626863645209, 2656815728257,
2664554418439, 2686829603333, 2695899652181, 2705406604801,
2707365603403, 2719578440833, 2727124432033, 2760910805521,
2767702208701, 2828440231781, 2834148920401, 2877700059361,
2879381407061, 2896154189281, 2925861537061, 2951748113693,
2967093653971, 2972440930681, 2975048100001, 2982748871681,
3018428185501, 3110610353203, 3114553625761, 3180009427489,
3207161943301, 3208502083333, 3219690385621, 3245148857411,
3270253512961, 3302306888833, 3310846205591, 3326810303041,
3342575384821, 3369163558661, 3379047167161, 3379796769721,
3383995047841, 3400612157801, 3400762888351, 3442386896033,
3444791080981, 3482365448801, 3495948351001, 3500661969001,
3522700695403, 3575736958993, 3591084112513, 3662237164657,
3675833369941, 3681968513653, 3689145811201, 3723670013671,
3732462022171, 3807483853889, 3816046640033, 3833498390881,
3867581146133, 3872097346081, 3873027365551, 3890395893781,
3897860696581, 3899209715497, 3917558112931, 3964270810937,
4005240325633, 4038238528133, 4063607975209, 4079372294401,
4094040693601, 4102653320641, 4110650869781, 4137703241629,
4225815030533, 4273732549633, 4291216861387, 4297203019831,
4311743149121, 4344230682241, 4370349054241, 4371702986509,
4390577128981, 4404641724001, 4408960528961, 4489003141699,
4492211878463, 4538380205633, 4563091603201, 4565807232209,
4582386169453, 4598439565807, 4607940316751, 4644875186407,
4664195570161, 4665115722511, 4703710453129, 4705672578881,
4758360794881, 4775786840833, 4890887858089, 4919511801007,
4983998542291, 5052122472403, 5055897021061, 5084590725521,
5107796180033, 5170276534483, 5184872575459, 5189337293141,
5189471610247, 5204101607717, 5223455560019, 5359215515851,
5394977100833, 5400288833633, 5426612329861, 5456559285731,
5462213919469, 5527428207961, 5542948103701, 5622012073861,
5629426501201, 5638270422881, 5641824409121, 5667892409051,
5678664030341, 5718605357921, 5741704355531, 5780725922791,
5826579567241, 5829429203333, 5889989144881, 5906557672019,
5945435620279, 5971351119931, 6024967051951, 6075265568789,
6079147854341, 6089474103101, 6144662561441, 6161684831641,
6171834715201, 6173851226401, 6181986492001, 6206900808907,
6244346078741, 6255755876231, 6287912246305, 6334121029633,
6401137442161, 6462876058501, 6464655094721, 6506450925391,
6523889941381, 6546463299427, 6552344768477, 6575954737169,
6580444368961, 6650940130721, 6672881536133, 6677514077001,
6801140706091, 6861127404773, 6882678712369, 6897572107471,
6914322587233, 6927066216533, 6951775474877, 6964186304701,
6985923908671, 7024285169441, 7055105322299, 7059453851341,
7098827220253, 7251580994401, 7355043315181, 7374879506611,
7378286917633, 7519478061061, 7530120865541, 7598850451501,
7627455792001, 7683425642353, 7690824875521, 7708256342561,
7720052083333, 7729741408201, 7745058800981, 7789632216181,
7822112133551, 7948459538251, 7972635335329, 7980978831701,
8018624827531, 8024126623801, 8065202624669, 8079048311041,
8083076499161, 8089036364503, 8191343376133, 8270890745941,
8419008492961, 8423274716033, 8426510545447, 8469480851287,
8483683350367, 8537842139401, 8589279856009, 8603092110649,
8610012346321, 8644361731963, 8660884022473, 8676148289621,
8688457754401, 8704517086721, 8716888633753, 8720978860651,
8723169633751, 8739867442561, 8843457876571, 8854362103051,
8904043716961, 8919725812003, 9047554019681, 9093897627781,
9213649032869, 9215601768229, 9279703419841, 9286935898411,
9295264185301, 9298834593751, 9308674934021, 9322948573121,
9324078086201, 9339075065633, 9369240439357, 9381870923041,
9463393537057, 9534925173271, 9606852012161, 9739862537437,
9740170453333, 9760657627841, 9818337142847, 9895467776833,
9967458388231, 10024729037317, 10030350985903, 10085416107541,
10093600101991, 10116657853849, 10165601371591, 10175363033921,
10190392639421, 10230727286413, ...



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