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Index to OEIS: Section Pri

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prime divisor, greatest: A006530
prime factorizations of important sequences: see factorizations of important sequences

prime factors, sequences related to :

prime factors: at least (1) 1: A000027 2: A002808 3: A033942 4: A033987 5: A046304

prime factors: at least (2) 6: A046305 7: A046307 8: A046309 9: A046311 10: A046313

prime factors: at most 1: A000040 2: A037143 3: A037144 4: A166718 5: A166719

prime factors: exactly (1) 1: A000040 2: A001358 3: A014612 4: A014613 5: A014614

prime factors: exactly (2) 6: A046306 7: A046308 8: A046310 9: A046312 10: A046314

prime factors: exactly (3) 11: A069272 12: A069273 13: A069274 14: A069275 15: A069276

prime factors: exactly (4) 16: A069277 17: A069278 18: A069279 19: A069280 20: A069281

prime factors: number of A001222

prime factors: see also distinct prime factors

prime factors: table of: A078840

prime numbers of measurement: A002048*, A002049*
prime numbers: A000040*, A008578
prime plus twice a square: A046903

prime powers, sequences related to :

prime powers: base: A025473, exponent: A025474

prime powers: complement of: A024619

prime powers: excluding primes: base: A025476, exponent: A025477

prime powers: excluding primes: complement of: A085971

prime powers: excluding primes: gaps: A053707

prime powers: excluding primes: gaps: record: A167186, start: A167188, end: A167189

prime powers: excluding primes: list of: A025475, previous: A167185, next: A167184

prime powers: excluding primes: number of: A085501

prime powers: gaps: A057820

prime powers: gaps: record: A121492, start: A002540, end: A167236

prime powers: list of: A000961, previous: A031218, next: A000015

prime powers: number of: A065515

prime pyramid: A051237*, A036440
Prime quadruplets:: A007530

prime races, sequences related to :

prime races: A007350, A007351, A007352, A007353, A007354, A007355, A096447, A096448, A096449, A096450, A096451, A096452, A096453, A096454, A096455, A098044

prime races: see also races

prime signature, sequences related to :

prime signature: A025487*

prime signature: see also (1) A000688 A005361 A008480 A008683 A008966 A025488 A035206 A035341 A036035 A036041 A038538 A046660

prime signature: see also (2) A046951 A050320 A050322 A050323 A050324 A050325 A050326 A050327 A050328 A050329 A050330 A050331

prime signature: see also (3) A050332 A050333 A050334 A050335 A050336 A050337 A050338 A050339 A050340 A050341 A050345 A050346

prime signature: see also (4) A050347 A050348 A050349 A050350 A050354 A050355 A050356 A050357 A050358 A050359 A050360 A050361

prime signature: see also (5) A050362 A050363 A050364 A050370 A050371 A050372 A050373 A050374 A050375 A050377 A050378 A050379

prime signature: see also (6) A050380 A050382 A051282 A051466 A051707 A052213 A052214 A052304 A052305 A052306 A056099 A056153

prime signature: see also (7) A056808 A056823 A057335

prime signature: see also (8) primes, in arithmetic progressions

prime triplets: A007529
prime(2^n): A033844*, A018249, A051438, A051440, A051439
prime(k^n): A033844, A038833, A119772, A055680, A058192, A058239, A119773, A119774, A006988, A058244, A058245, A058246, A119775, A119776, A119777
prime(n) == +/-k (mod n): (1) A023143, A023144, A023145, A023146, A023147, A023148, A023149, A023150, A023151, A023152, A049204, A092044
prime(n) == +/-k (mod n): (2) A092045, A092046, A092047, A092048, A092049, A092050, A092051, A092052
prime, largest <=n: A007917
prime, largest dividing n: A006530
prime, smallest whose product of digits is (something): A088653 A088654 A089298 A089364 A089365 A089386 A089912
prime, weakly: A050249
PRIMEGAME: A007542, A007546, A007547
PrimePi(x), number of primes <= x: A000720*

primes , sequences related to :

primes : A000040*

primes gaps, see primes, gaps between

primes in Lucas U-sequences: A049883 U(1,-2), A005478 U(1,-1), A086383 U(2,-1), A000040 U(2,1), A201000 U(3,-2), A201001 U(3,-1), A000668 U(3,2), A076481 U(4,3), A201002 U(5,-2), A201005 U(5,-1)

primes in arithmetic progressions, see primes, in arithmetic progressions

primes involving quasi-repdigits D(R)nE: (01) A049054, A088274, A088275, A102929, A102930, A102931, A102932, A102933, A102934, A102935,

primes involving quasi-repdigits D(R)nE: (02) A102936, A102937, A102938, A102939, A102940, A102941, A102942, A102943, A102944, A102945,

primes involving quasi-repdigits D(R)nE: (03) A102946, A102947, A081677, A101392, A102948, A102949, A102950, A102951, A102952, A102953,

primes involving quasi-repdigits D(R)nE: (04) A102954, A102955, A098930, A099006, A102956, A098959, A102957, A098960, A102958, A102959,

primes involving quasi-repdigits D(R)nE: (05) A102959, A102960, A102961, A102962, A102963, A102964, A056807, A100501, A101393, A102965,

primes involving quasi-repdigits D(R)nE: (06) A102966, A102967, A102968, A102969, A102970, A102971, A102972, A102973, A102974, A102975,

primes involving quasi-repdigits D(R)nE: (07) A102976, A102977, A102978, A102979, A102980, A101396, A101398, A056806, A101397, A101395,

primes involving quasi-repdigits D(R)nE: (08) A101394, A102981, A102982, A102983, A102984, A102985, A102986, A102987, A102988, A102989,

primes involving quasi-repdigits D(R)nE: (09) A102990, A102991, A102992, A102993, A102994, A099005, A099017, A102995, A102996, A102997,

primes involving quasi-repdigits D(R)nE: (10) A102998, A102999, A103000, A103001, A103002, A103003, A096254, A103004, A103005, A103006,

primes involving quasi-repdigits D(R)nE: (11) A103007, A103008, A103009, A103010, A103011, A103012, A103013, A103014, A103015, A103016,

primes involving quasi-repdigits D(R)nE: (12) A103017,A103018,A103019,A103020,A103021,A103022,A103023,A103024,A103025,A056805,

primes involving quasi-repdigits D(R)nE: (13) A103027,A103027,A103028,A103029,A103030,A097402,A103031,A103032,A103033,A103034,

primes involving quasi-repdigits D(R)nE: (14) A103035,A103036,A103037,A103038,A103039,A103040,A103041,A103042,A103043,A103044,

primes involving quasi-repdigits D(R)nE: (15) A103045,A103046,A103047,A103048,A103049,A056804,A097970,A097954,A103050,A103051,

primes involving quasi-repdigits D(R)nE: (16) A103052,A103053,A103054,A103055,A103056,A103057,A103058,A103059,A103060,A103061,

primes involving quasi-repdigits D(R)nE: (17) A103062,A103063,A103064,A103065,A103066,A103067,A103068,A099190,A103069,A103070,

primes involving quasi-repdigits D(R)nE: (18) A103071,A103072,A103073,A103074,A103075,A103076,A103077,A103078,A103079,A103080,

primes involving quasi-repdigits D(R)nE: (19) A103081,A103082,A103083,A103084,A103085,A103086,A103087,A103088,A103089,A103090,

primes involving quasi-repdigits D(R)nE: (20) A103091,A103092,A056797,A096774,A100473,A103093,A103094,A103095,A103096,A103097,

primes involving quasi-repdigits D(R)nE: (21) A103098,A103099,A103100,A103101,A103102,A103103,A103104,A103105,A103106,A103107,

primes involving quasi-repdigits D(R)nE: (22) A103108,A103109

primes involving repunits , sequences related to :

primes involving repunits, X*10*repunits+Y: (1): A004023, A056654, A056655, A056659, A056660, A056656, A056677, A056678, A055520, A056680,

primes involving repunits, X*10*repunits+Y: (2): A056681, A056661, A056682, A056683, A056684, A056685, A056686, A056687, A056658, A056657,

primes involving repunits, X*10*repunits+Y: (3): A056688, A056689, A056693, A056664, A056694, A056695, A056663, A056696, A056662

primes involving repunits, X*10^n+Y*repunits: (1): A004023, A056698, A089147, A002957, A056700, A056701, A056702, A056703, A056704,

primes involving repunits, X*10^n+Y*repunits: (2): A056705, A056706, A056707, A056708, A056712, A056713, A056714, A056715, A056716,

primes involving repunits, X*10^n+Y*repunits: (3): A056717, A056718, A056719, A056720, A056721, A056722, A056723, A056724, A056725,

primes involving repunits, X*10^n+Y*repunits: (4): A056726, A056727

primes involving repunits, X*repunits+-Y: (1): A004023, A097683, A097684, A097685, A084832, A096506, A099409, A099410, A055557, A099411,

primes involving repunits, X*repunits+-Y: (2): A099412, A096845, A099413, A099414, A099415, A099416, A099417, A099418, A098088, A096507,

primes involving repunits, X*repunits+-Y: (3): A099419, A099420, A098089, A099421, A099422, A096846, A096508, A095714, A089675

primes of the form binomial(k*n, n) +- 1, k=2..6: A066699, A066726, A125221, A125220, A125241, A125240, A125243, A125242, A125245, A125244

primes p such that x^k = 2 has a solution mod p, sequences related to :

primes p such that x^k = 2 has a solution mod p, (**) means the divergence occurs beyond the last entry shown in the OEIS.

primes p such that x^k = 2 has a solution mod p, k=02 to 09: A038873 (or A001132), A040028, A040098, A040159, A040992, A042966, A045315(**), A049596,

primes p such that x^k = 2 has a solution mod p, k=10 to 19: A049542, A049543, A049544, A049545, A049546, A049547, A045315, A049549, A049550, A049551

primes p such that x^k = 2 has a solution mod p, k=20 to 29: A049552, A049553, A049554, A049555, A049556, A049557, A049558, A049596(**), A049560, A049561

primes p such that x^k = 2 has a solution mod p, k=30 to 39: A049562, A000040(**), A049564, A049565, A049566, A049567, A049568, A049569, A049570, A049571

primes p such that x^k = 2 has a solution mod p, k=40 to 49: A049572, A049573, A049574, A058853, A049576, A049577, A049578, A000040(**), A049580, A042966(**)

primes p such that x^k = 2 has a solution mod p, k=50 to 59: A049582, A049583, A049584, A049585, A049550(**), A049587, A049588, A049589, A049590, A000040(**)

primes p such that x^k = 2 has a solution mod p, k=60 to 63: A049592, A000040(**), A049594, A049595

primes such that the sum of the predecessor and successor primes is divisible by k: A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158

primes that become a different prime under some mapping

see also: primes, sequences related to decimal representation of (to be created), digits, maps acting on (to be created).

primes that become a different prime under some mapping (1): A180533 A180535 A180537 A180560 A180541 A180543 A180552 A180581 A180561 A180530 A180526 A180527

primes that become a different prime under some mapping (2): A180545 A180525 A180528 A180531 A180559 A180529 A180532 A180538 A180534 A180517 A180540 A180542

primes that become a different prime under some mapping (3): A180518 A180548 A180547 A180519 A180546 A180549 A180550 A180553 A180520 A180555 A180557 A180521

primes that become a different prime under some mapping (4): A180558 A180522 A180523 A180524 A180536 A180539 A180544 A180554 A180551 A180556

primes with given smallest positive primitive root

primes with X as smallest positive primitive root: (1) A001122, A001123, A001124, A001125, A001126, A061323, A061324, A061325, A061326, A061327,

primes with X as smallest positive primitive root: (2) A061328, A061329, A061330, A061331, A061332, A061333, A061334, A061335, A061730, A061731,

primes with X as smallest positive primitive root: (3) A061732, A061733, A061734, A061735, A061736, A061737, A061738, A061739, A061740, A061741,

primes with X as smallest positive primitive root: (4) A114657, A114658, A114659, A114660, A114661, A114662, A114663, A114664, A114665, A114666,

primes with X as smallest positive primitive root: (5) A114667, A114668, A114669, A114670, A114671, A114672, A114673, A114674, A114675, A114676,

primes with X as smallest positive primitive root: (6) A114677, A114678, A114679, A114680, A114681, A114682, A114683, A114684, A114685, A114686

primes, <= n: A000720*

primes, absolute: A003459*

primes, additive: A046704

primes, almost: see almost primes

primes, approximations to: A050503, A050502, A050504

primes, arithmetic progressions of, see primes, in arithmetic progressions

primes, automorphic: A046883, A046884

primes, balanced: (index) A096693, A096705, A096706, A096707, A096708, A096697, A096709, A096695

primes, balanced: (order) A006562, A082077, A082078, A082079, A096697, A096698, A096699, A096700, A096701, A096702,

primes, balanced: (order) A096703, A096704, A081415, A082080, A126554, A096692, A127557, A096696, A160920, A090403

primes, balanced: (order) A126556, A126558, A126555, A126557, A127364, A126559, A051795, A054342, A090403, A055206

primes, balanced: A006562, A051795, A054342

primes, Bertrand: A006992*, A051501

primes, Bertrand: see also Bertrand's Postulate

Primes, by class number, A002148, A002142, A002146, A002147, A002149

primes, by Erdos-Selfridge class n+: (0) A005113, A126433, A101253

primes, by Erdos-Selfridge class n-: (0) A056637, A101231, A126805

primes, by Erdos-Selfrigde class n+: (1) A005105, A005106, A005107, A005108, A081633, A081634

primes, by Erdos-Selfrigde class n+: (2) A081635, A081636, A081637, A081638, A081639, A084071, A090468, A129474, A129475

primes, by Erdos-Selfrigde class n-: (1) A005109, A005110, A005111, A005112, A081424, A081425

primes, by Erdos-Selfrigde class n-: (2) A081426, A081427, A081428, A081429, A081430, A081640, A081641, A129248, A129249, A129250

Primes, by number of digits, A003617, A006879, A006880, A003618

primes, by order: (1) A007821, A049078, A049079, A049080, A049081, A058322, A058324, A058325, A058326, A058327, A058328, A093046

primes, by order: (2) A000040, A006450, A038580, A049090, A049203, A049202, A057849, A057850, A057851, A057847, A058332, A093047

Primes, by period length, A007615

primes, by primitive root , sequences related to :

primes, by primitive root: (01) A001122 A001123 A001124 A001125 A001126 A001913 A002230 A003147 A007348 A007349 A019334 A019335

primes, by primitive root: (02) A019336 A019337 A019338 A019339 A019340 A019341 A019342 A019343 A019344 A019345 A019346 A019347

primes, by primitive root: (03) A019348 A019349 A019350 A019351 A019352 A019353 A019354 A019355 A019356 A019357 A019358 A019359

primes, by primitive root: (04) A019360 A019361 A019362 A019363 A019364 A019365 A019366 A019367 A019368 A019369 A019370 A019371

primes, by primitive root: (05) A019372 A019373 A019374 A019375 A019376 A019377 A019378 A019379 A019380 A019381 A019382 A019383

primes, by primitive root: (06) A019384 A019385 A019386 A019387 A019388 A019389 A019390 A019391 A019392 A019393 A019394 A019395

primes, by primitive root: (07) A019396 A019397 A019398 A019399 A019400 A019401 A019402 A019403 A019404 A019405 A019406 A019407

primes, by primitive root: (08) A019408 A019409 A019410 A019411 A019412 A019413 A019414 A019415 A019416 A019417 A019418 A019419

primes, by primitive root: (09) A019420 A019421 A029932 A047933 A047934 A047935 A047936 A048975 A048976 A066529 A023048

primes, by primitive root: (09) A105874-A105914

primes, by primitive root: see also Artin's constant

Primes, chains of, A005603, A005602

primes, characteristic function of: A010051

Primes, compressed, A002036

primes, concatenation of: A033308

Primes, consecutive, A006549, A007700, A007513, A007529, A007530, A006489

primes, cuban: A002407*, A002648, A002504, A001479, A001480, A002367, A002368

primes, cuban, generalized: A007645*, A003627, A217035

primes, cuban, see also: A159961, A113478, A221717, A221793

primes, Cullen: A005849*, A050920*

primes, deceptive: A000864

Primes, decompositions into, A002375, A002126, A001031, A002372, A007414

primes, differences between: A001223*, A007921*, A030173*, A037201

primes, differences between: see also primes, gaps between

primes, dihedral calculator: A038136

primes, dihedral palindromic: A048662

primes, dividing n: A001221*, A001222*, A006530*, A046660

primes, doubled: A001747, A005602, A005603

primes, duodecimal: A006687

primes, Euclid-Pocklington: A053341*

primes, Euclidean: A007996

primes, even: A001747

primes, factorial: see factorial primes

primes, Fermat, generalized, see primes, generalized Fermat

primes, Fermat, generalized: A056993* A005574 A000068 A006314 A006313 A006315 A006316 A056994 A056995 A057465 A057002 A088361 A088362

primes, Fermat: A019434*, A050922

primes, Fermat: see also A093625, A138083, A171381

primes, Fibonacci numbers: A001605*, A005478*

primes, final digits of: A007652

primes, fortunate, A005235

primes, from Euclid's proof: A000945*, A000946*

primes, gaps between , sequences related to :

primes, gaps between, A001223*, A007921*, A030173*, A037201, A023200

primes, gaps between: primes beginning gaps of sizes 2, 4, ..., 64 are given in A001359, A029710, A031924, A031926, A031928 (gap 10), A031930, A031932, A031934, A031936, A031938 (gap 20), A061779, A098974, A124594, A124595, A124596 (gap 30), A126784, A134116, A134117, A134118, A126721 (gap 40), A134120, A134121, A134122, A134123, A134124 (gap 50), A204665, A204666, A204667, A204668, A126771 (gap 60), A204669, A204670.

primes, gaps between: primes beginning gaps of 70, 80,... 200: A204792, A126722, A204764, A050434 (gap 100), A204801, A204672 (gap 120), A204802, A204803, A126724 (gap 150), A184984, A204805, A204673 (gap 180), A204806, A204807 (gap 200)

primes, gaps between: start of the first gap of 2n: A000230, 6n: A058193, 10n: A140791, 2^n: A062529, 10^n: A101232, n^2: A138198, a^b: A123995, 128: A204812, 256: A204813.

primes, gaps between: twin primes and related: A001359, A006512, A077800, A001097, A049591

primes, gaps between, A031924 A031925 A031926 A031927 A031928 A031929 A031930 A031931 A031932 A031933 A031934 A031935 A031936 A031937 A031938 A031939

primes, gaps between, LCM of: A080374 A080375 A080376 A083273 A083552 A083551

primes, gaps between, records for: A000101* (upper end), A002386* (lower end), A005250* (gaps)

primes, gaps between, see also: A124582-A124591, A005669, A002540, A000232, A001549, A001632

primes, gaps between, see also: primes, differences between

primes, generalized Fermat: A006686, A078902, A090874, A100266, A100267, A123646

primes, generated by polynomials: see primes, produced by polynomials

primes, Germain: see primes, Sophie Germain

primes, good: A046869, A028388

primes, half-quartan: A002646

primes, happy: A035497

primes, Higgs: A007459

primes, home: A037274* (base 10), A048986* and A064795 (base 2)

primes, home, see also A048985, A064841, A195264

primes, Honaker: A033548

primes, iccanobiF: A036797

primes, in arithmetic progressions, sequences related to :

primes, in arithmetic progressions: (01) Consider n-term arithmetic progressions (APs) of primes, i, i+d, i+2d, ..., i+(n-1)d. We can minimize (a) the first term i, (b) the common difference d, or (c) the last term, l=i+(n-1)d. This gives rise to 12 sequences since for each problem we can list the values of i, d, l, and we can list the progressions as the rows of a triangle:

primes, in arithmetic progressions: (02) problem (a) i: A007918* (assuming k-tuple conjecture), d: A061558, l: A120302, triangle: A130791

primes, in arithmetic progressions: (03) problem (b) i: A033189, d: A033188*, l: A113872, triangle: A133276

primes, in arithmetic progressions: (04) problem (c) i: A113827, d: A093364, l: A005115*, triangle: A133277

primes, in arithmetic progressions: (05) If we take the initial value to be the n-th prime (A000040) the the sequences are: d: A088430, l: A113834, triangle: A133278

primes, in arithmetic progressions: (06) One may also ask for n consecutive primes in arithmetic progression: this gives A006560

primes, in arithmetic progressions: (07) One may also consider n consecutive numbers in arithmetic progression having the same prime signature, and ask the same questions. This gives the following sequences:

primes, in arithmetic progressions: (08) problem (a) i: A133279, d: A113461, l: A127781, triangle: A113460

primes, in arithmetic progressions: (09) problem (b) i: A034173, d: the all-ones sequence A000012, l: A034174, triangle: A083785

primes, in arithmetic progressions: (10) problem (c) i: A087308, d: A087310, l: A133280, triangle: A086786

primes, in arithmetic progressions: (11) One may also ask for n consecutive numbers with the same prime signature: this gives sequences A034173, A034174, A083785 again. See also A087307

primes, in arithmetic progressions: (12) See also A031217 A033168 A033290 A033446 A033447 A033448 A033449 A033450

primes, in arithmetic progressions: (13) See also A033451 A035050 A035089 A035091 A035092 A035093 A035094 A035095 A035096 A047980 A047981 A047982

primes, in arithmetic progressions: (14) See also A052239 A052242 A052243 A053647 A054203 A057324 A057325 A057326 A057327 A057328 A057329 A057330

primes, in arithmetic progressions: (15) See also A057331 A057778 A057874 A058252 A058323 A058362 A059044

primes, in arithmetic progressions: (16) Higher powers: A001912, A002496, A005574, A115104, A199307, A199364, A199365, A199366, A199367, A199368, A199369

primes, in decimal expansion of Pi: A005042

Primes, in intervals, A007491

Primes, in number fields, A003631, A003625, A003628, A003630, A003632, A003626

Primes, in residue classes, A003627, A002313, A003629, A002145, A007520, A002515, A007528, A002144, A007521, A002476, A001132, A007522, A007519

Primes, in sequences, A003032, A003033, A002072

Primes, in ternary, A001363

primes, in various ranges , sequences related to :

primes, in various ranges: (1) A003604 A006879 A006880 A007053 A007508 A033843 A035533 A036351 A036386 A039506 A039507

primes, in various ranges: (2) A040014 A049035 A049040 A050251 A050258 A050986 A050987 A052130 A055206 A055552 A055683 A055728

primes, in various ranges: (3) A055729 A055730 A055731 A055732 A055737 A055738 A057573 A057978 A058191 A058247 A058248 A060969

primes, in various ranges: (4) A060970 A060971 A063501 A064151 A066265 A066873 A071973

primes, in various ranges: (5) A091644 A091645 A091646 A091647 A091705 A091706 A091707 A091708 A091709 A091710

primes, in various ranges: (6) A091634 A091635 A091636 A091637 A091638 A091639 A091640 A091641 A091642 A091643

Primes, inert, A003631, A003625, A003628, A003630, A003632, A003626

primes, irregular: A000928*, A061576*

Primes, isolated, A007510

primes, isolated: A039818

Primes, largest, A006530, A006990, A007014, A002374, A003618

primes, left-truncatable: see truncatable primes

primes, lonely: A023186, A023187, A023188

primes, long period: A006883*

primes, Lucas numbers: A001606*, A005479*

primes, Lucasian: A002515*

primes, Mersenne: A000668* (primes of form 2^p-1), A000043* (p values)

primes, Mills's: A051254*

primes, minus a constant: A000040*, A014689, A014692, A040976

primes, multiplicative and additive: A046713

primes, multiplicative: A046703

primes, next: A007918

primes, number of less than k^n: A007053, A055729, A086680, A055730, A055731, A055732, A086681, A086682, A006880, A058247, A058248, A058191

primes, number of less than n*10^k: (1) A000720*, A038801, A028505, A038812, A038813, A038814, A038815, A038816, A038817, A038818, A038819,

primes, number of less than n*10^k: (2) A038820, A038821, A038822, A080123, A080124, A080125, A080126, A080127, A080128, A080129, A116356

primes, octavan: A006686

primes, of a particular form, number that are less than or equal to 10^n: A091115 A091116 A091117 A091119-A091129 A091099 A091098 A006880 A007508

primes, of form k*n! +- 1: (1) A002981, A002982, A051915, A076133, A076679, A076134, A076680, A099350, A076681, A099351,

primes, of form k*n! +- 1: (2) A076682, A180627, A076683, A180628, A180625, A180629, A180626, A180630, A126896, A180631

primes, of form n! +- 1: A002981, A002982

primes, of form x^2 + kxy + y^2: (1) A007519 A007645 A033212 A033215 A038872 A068228 A107008 A107008 A107145 A107152 A139492 A139493

primes, of form x^2 + kxy + y^2: (2) A139493 A139494 A139495 A139496 A139497 A139498 A139499 A139500 A139501 A139502 A139503 A139504

primes, of form x^2 + kxy + y^2: (3) A139505 A139506 A139507 A139508 A139509 A139510 A139511 A139512

primes, of form x^2+27y^2: A014752, A040028

primes, of form x^2+y^2: A002313*, A002331, A002330, A002144

primes, order of: A049076, A007097

primes, palindromic: A002385*, A007500, A007616

primes, palindromic: see also (1) A016041 A029971 A029972 A029973 A029974 A029975 A029976 A029977 A029978 A029979 A029980 A029981

primes, palindromic: see also (2) A029982 A029732 A046942 A046941 A050236 A050239 A039954 A118064 A119351 A016115 A050251 A050683

primes, palindromic, smoothly undulating, sequences related to :

primes, palindromic, smoothly undulating, A062209 A062210 A062211 A062212 A062213 A062214 A062215 A062216 A062217 A062218 A062219 A062220

primes, palindromic, smoothly undulating, A062221 A062222 A062223 A062224 A062225 A062226 A062227 A062228 A062229 A062230 A062231 A062232

primes, palindromic, smoothly undulating, A077799 A059758 A032758

primes, period of reciprocal of, see 1/p

primes, Pierpont: A005109

Primes, primitive roots of, A001918, A002233, A002199, A002231, A001122, A007348, A003147, A001913, A001123, A007349, A001124, A001125, A001126

primes, produced by polynomials, etc.: A050268, A121887, A139414, A033189

Primes, products of, A007467, A006881, A006094, A007304

primes, products of: A000040 (1), A001358 (2), A014612 (3), A014613 (4)

primes, pseudo: see pseudoprimes

primes, quadratic form, discriminant -104: A107132, A033218

primes, quadratic form, discriminant -108: A014752

primes, quadratic form, discriminant -112: A107133, A107134

primes, quadratic form, discriminant -116: A033219

primes, quadratic form, discriminant -11: A056874, A106857

primes, quadratic form, discriminant -120: A107135, A107136, A107137, A033220

primes, quadratic form, discriminant -124: A033221

primes, quadratic form, discriminant -128: A105389

primes, quadratic form, discriminant -12: A002476

primes, quadratic form, discriminant -132: A107138, A033222

primes, quadratic form, discriminant -136: A107139, A033223

primes, quadratic form, discriminant -140: A107140, A033224

primes, quadratic form, discriminant -144: A107141, A107142

primes, quadratic form, discriminant -148: A033225

primes, quadratic form, discriminant -152: A107143, A033226

primes, quadratic form, discriminant -156: A033227

primes, quadratic form, discriminant -15: A033212, A106858, A106859, A106860, A106861

primes, quadratic form, discriminant -160: A107144, A107145

primes, quadratic form, discriminant -164: A033228

primes, quadratic form, discriminant -168: A107146, A107147, A107148, A033229

primes, quadratic form, discriminant -16: A002144, A002313

primes, quadratic form, discriminant -172: A033230

primes, quadratic form, discriminant -176: A107149, A107150

primes, quadratic form, discriminant -180: A107151, A107152

primes, quadratic form, discriminant -184: A107153, A033231

primes, quadratic form, discriminant -188: A033232

primes, quadratic form, discriminant -192: A107154

primes, quadratic form, discriminant -196: A107155

primes, quadratic form, discriminant -19: A106862, A106863

primes, quadratic form, discriminant -200: A107156, A107157

primes, quadratic form, discriminant -204: A107158, A033233

primes, quadratic form, discriminant -208: A107159, A107160

primes, quadratic form, discriminant -20: A033205, A106864, A106865

primes, quadratic form, discriminant -212: A033234

primes, quadratic form, discriminant -216: A107161, A107162

primes, quadratic form, discriminant -220: A033235

primes, quadratic form, discriminant -224: A107163, A107164

primes, quadratic form, discriminant -228: A107165, A033236

primes, quadratic form, discriminant -232: A107166, A033237

primes, quadratic form, discriminant -236: A033238

primes, quadratic form, discriminant -23: A106866, A106867, A106868, A106869

primes, quadratic form, discriminant -240: A107167, A107168, A107169

primes, quadratic form, discriminant -244: A033239

primes, quadratic form, discriminant -248: A107170, A033240

primes, quadratic form, discriminant -24: A033199, A084865

primes, quadratic form, discriminant -256: A014754

primes, quadratic form, discriminant -260: A107171, A033241

primes, quadratic form, discriminant -264: A107172, A107173, A107174, A033242

primes, quadratic form, discriminant -268: A033243

primes, quadratic form, discriminant -272: A107175, A107176

primes, quadratic form, discriminant -276: A107177, A033244

primes, quadratic form, discriminant -27: A002476, A106870

primes, quadratic form, discriminant -280: A107178, A107179, A107180, A033245

primes, quadratic form, discriminant -284: A033246

primes, quadratic form, discriminant -288: A107181

primes, quadratic form, discriminant -28: A033207

primes, quadratic form, discriminant -292: A033247

primes, quadratic form, discriminant -296: A107182, A033248

primes, quadratic form, discriminant -300: A107183, A107184

primes, quadratic form, discriminant -304: A107185, A107186

primes, quadratic form, discriminant -308: A107187, A033249

primes, quadratic form, discriminant -312: A107188, A107189, A107190, A033250

primes, quadratic form, discriminant -316: A033251

primes, quadratic form, discriminant -31: A033221, A106871, A106872, A106873, A106874

primes, quadratic form, discriminant -320: A107191, A107192

primes, quadratic form, discriminant -324: A107193

primes, quadratic form, discriminant -328: A107194, A033252

primes, quadratic form, discriminant -32: A007519, A007520, A106875, A106876

primes, quadratic form, discriminant -332: A033253

primes, quadratic form, discriminant -336: A107195, A107196, A107197, A107198

primes, quadratic form, discriminant -340: A107199, A033254

primes, quadratic form, discriminant -344: A107200, A033255

primes, quadratic form, discriminant -348: A033256

primes, quadratic form, discriminant -352: A107201, A107202

primes, quadratic form, discriminant -356: A033257

primes, quadratic form, discriminant -35: A106877, A106878, A106879, A106880, A106881

primes, quadratic form, discriminant -360: A107203, A107204, A107205, A107206

primes, quadratic form, discriminant -364: A107207, A033258

primes, quadratic form, discriminant -368: A107208, A107209

primes, quadratic form, discriminant -36: A040117, A068228, A106882

primes, quadratic form, discriminant -372: A107210, A033202

primes, quadratic form, discriminant -376: A107211, A033204

primes, quadratic form, discriminant -380: A033206

primes, quadratic form, discriminant -384: A107212, A107213

primes, quadratic form, discriminant -388: A033208

primes, quadratic form, discriminant -392: A107214, A107215

primes, quadratic form, discriminant -396: A107216, A107217

primes, quadratic form, discriminant -39: A033227, A106883, A106884, A106885, A106886, A106887, A106888

primes, quadratic form, discriminant -3: A007645

primes, quadratic form, discriminant -400: A107218, A107219

primes, quadratic form, discriminant -40: A033201, A106889

primes, quadratic form, discriminant -43: A106890, A106891

primes, quadratic form, discriminant -44: A033209, A106282, A106892, A106893

primes, quadratic form, discriminant -47: A033232, A106894, A106895, A106896, A106897, A106898, A106899, A106900

primes, quadratic form, discriminant -48: A068229

primes, quadratic form, discriminant -4: A002313

primes, quadratic form, discriminant -51: A106901, A106902, A106903, A106904

primes, quadratic form, discriminant -52: A033210, A106905, A106906

primes, quadratic form, discriminant -55: A033235, A106907, A106908, A106909, A106910, A106911, A106912, A106913

primes, quadratic form, discriminant -56: A033211, A106914, A106915, A106916, A106917

primes, quadratic form, discriminant -59: A106918, A106919, A106920, A106921, A106922

primes, quadratic form, discriminant -63: A106923, A106924, A106925, A106926, A106927, A106928, A106929, A106930

primes, quadratic form, discriminant -64: A007521, A106931

primes, quadratic form, discriminant -67: A106932, A106933

primes, quadratic form, discriminant -68: A033213, A106934, A106935, A106936, A106937, A106938

primes, quadratic form, discriminant -71: A033246, A106939, A106940, A106941, A106942, A106943, A106944, A106945, A106946, A106947, A106948

primes, quadratic form, discriminant -72: A106949, A106950

primes, quadratic form, discriminant -75: A033212, A106951, A106952

primes, quadratic form, discriminant -76: A033214, A106953, A106954, A106955

primes, quadratic form, discriminant -79: A033251, A106956, A106957, A106958, A106959, A106960, A106961, A106962

primes, quadratic form, discriminant -7: A045373, A106856

primes, quadratic form, discriminant -80: A047650, A106963, A106964, A106965

primes, quadratic form, discriminant -83: A106966, A106967, A106968, A106969, A106970

primes, quadratic form, discriminant -84: A033215, A102271, A102273, A106971, A106972, A106973, A106974

primes, quadratic form, discriminant -87: A033256, A106975, A106976, A106977, A106978, A106979, A106980, A106981, A106982, A106983

primes, quadratic form, discriminant -88: A033216, A106984

primes, quadratic form, discriminant -8: A033203

primes, quadratic form, discriminant -91: A106985, A106986, A106987, A106988, A106989

primes, quadratic form, discriminant -92: A033217

primes, quadratic form, discriminant -95: A033206, A106990, A106991, A106992, A106993, A106994, A106995, A106996, A106997, A106998, A106999, A107000, A107001

primes, quadratic form, discriminant -96: A107002, A107003, A107004, A107005, A107006, A107007, A107008

primes, quadratic form, discriminant -99: A107009, A107010, A107011, A107012, A107013

primes, quadratic form, discriminant 1020: A139512

primes, quadratic form, discriminant 117: A139494

primes, quadratic form, discriminant 140: A139495

primes, quadratic form, discriminant 165: A139496

primes, quadratic form, discriminant 21: A139492

primes, quadratic form, discriminant 221: A139497

primes, quadratic form, discriminant 285: A139498

primes, quadratic form, discriminant 357: A139499

primes, quadratic form, discriminant 396: A139500

primes, quadratic form, discriminant 437: A139501

primes, quadratic form, discriminant 480: A139502

primes, quadratic form, discriminant 525: A139503

primes, quadratic form, discriminant 572: A139504

primes, quadratic form, discriminant 621: A139505

primes, quadratic form, discriminant 672: A139506

primes, quadratic form, discriminant 725: A139507

primes, quadratic form, discriminant 77: A139493

primes, quadratic form, discriminant 780: A139508

primes, quadratic form, discriminant 837: A139509

primes, quadratic form, discriminant 896: A139510

primes, quadratic form, discriminant 957: A139511

Primes, quadratic partitions of, A002973, A002972

Primes, quadratic residues of, A002223, A002224, A002225, A002226, A002228, A002227

primes, quartan: A002645

primes, quintan: A002649, A002650

primes, reciprocals of, periods: see 1/p

primes, regular: A007703*

Primes, represented by quadratic forms, A002496, A007645, A002383, A007490, A002327, A005473, A005471, A007635, A007639, A007637, A007641, A005846

primes, repunit: A004022*, A004023*

primes, right-truncatable: see truncatable primes

primes, safe: A005385*, A051900, A051901, A051902

primes, sextan: A002647

primes, short period: A006559*

Primes, single, A007510

primes, Sophie Germain: A005384

Primes, special sequences of, A001259, A001275

Primes, square roots of, A000006

primes, Stern: A042978

primes, strobogrammatic: A007597, A018847

primes, strong: A051634

primes, sum of the first k^n primes, k=2,3,5,6,7,10: A099825, A099826, A113633, A113634, A113635, A099824

Primes, sums of digits of, A007605

Primes, sums of, A007610, A001414, A007504, A007468, A002373, A001043, A001172

primes, sums of, minimizing: A022894, A083309, A113040, A215036, A215029, A215030

Primes, supersingular, A006962

primes, that divide sum of all primes <= p: A007506, A024011, A028581, A028582

Primes, to odd powers only, A002035

primes, transformed by cellular automata: A093510 A093511 A093512 A093513 A093514 A093515 A093516 A093517

primes, transforms of, A007442, A007444, A007447, A007441, A007445, A007296, A007446

primes, truncatable: see truncatable primes

primes, truncated: see truncatable primes

primes, twin primes conjecture: see also A093483

primes, twin: A001359*, A014574*, A006512*, A001097*, A077800

primes, twin: see also twin primes constant

primes, twin: see also A005597, A007508, A033843, A036061, A036062, A036063

primes, undulating: A039944

primes, various subsets in range 2^n,2^(n+1) , sequences related to :

primes, various subsets in range 2^n,2^(n+1), (numbers in parentheses give the primes whose occurrences are being counted)

primes, various subsets in range 2^n,2^(n+1): (1) A036378* (A000040), A095005 (A027697), A095006 (A027699), A095007 (A002144)

primes, various subsets in range 2^n,2^(n+1): (2) A095008 (A002145), A095009 (A007519), A095010 (A007520), A095011 (A007521), A095012 (A007522), A095013 (A001132), A095014 (A003629)

primes, various subsets in range 2^n,2^(n+1): (3) A095015 (A002476), A095016 (A007528), A095017 (A001359), A095018 (A066196), A095019 (A095071), A095020 (A095070), A095021 (A030430)

primes, various subsets in range 2^n,2^(n+1): (4) A095022 (A030432), A095023 (A030431), A095024 (A030433), A095052 (A095072), A095053 (A095073), A095054 (A095074), A095055 (A095075)

primes, various subsets in range 2^n,2^(n+1): (5) A095056 (A081091), A095057 (A095077), A095058 (A095078), A095059 (A095079), A095060 (A095080), A095061 (A095081), A095062 (A095082)

primes, various subsets in range 2^n,2^(n+1): (6) A095063 (A095083), A095064 (A095084), A095065 (A095085), A095066 (A095086), A095067 (A095087), A095068 (A095088), A095069 (A095089)

primes, various subsets in range 2^n,2^(n+1): (7) A095092 (A095102), A095093 (A095103), A095094 (A080114), A095095 (A080115)

primes, weak: A051635

primes, weakly prime numbers: A050249

primes, which are average of their neighbors: A006562

primes, whose reversal is a square, A007488

primes, Wilson: A007540*

Primes, with consecutive digits, A006510, A006055

primes, with embedded primes (permutation): A039993, A080603, A080608.

primes, with embedded primes (substring) (1): A033274, A034844, A039992, A039994, A039996, A039998, A045719, A079397, A092621, A092622,

primes, with embedded primes (substring) (2): A092623, A092628, A109066, A134596, A137812, A152313, A152426, A152427, A155024, A168169,

primes, with embedded primes (substring) (3): A178596, A178597, A179336, A179909, A179910, A179911, A179912, A179913, A179914, A179915,

primes, with embedded primes (substring) (4): A179916, A179917, A179918, A179919, A179920, A179922, A179924*

primes, with first digit 1 (or 2, 3, etc.): A045707, A045708, A045709, etc.

Primes, with large least nonresidues, A002225, A002226, A002228, A002227

Primes, with prime subscripts, A006450

primes, Woodall: A002234*, A050918*

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, sequences related to :

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (01): A000043 A001770 A001771 A001772 A001773 A001774 A001775 A002235 A002236 A002237 A002238 A002240

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (02): A002242 A002253 A002254 A002256 A002258 A002259 A002261 A002269 A002274 A032353 A032356 A032359

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (03): A032360 A032361 A032362 A032363 A032364 A032365 A032366 A032367 A032368 A032370 A032371 A032372

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (04): A032373 A032374 A032375 A032376 A032377 A032379 A032380 A032381 A032382 A032383 A032384 A032385

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (05): A032386 A032387 A032388 A032389 A032390 A032391 A032392 A032393 A032394 A032395 A032396 A032397

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (06): A032398 A032399 A032400 A032401 A032402 A032403 A032404 A032405 A032406 A032407 A032408 A032409

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (07): A032410 A032411 A032412 A032413 A032414 A032415 A032416 A032417 A032418 A032419 A032420 A032421

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (08): A032422 A032423 A032424 A032425 A032453 A032454 A032455 A032456 A032457 A032458 A032459 A032460

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (09): A032461 A032462 A032464 A032465 A032466 A032467 A032468 A032469 A032470 A032471 A032472 A032473

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (10): A032474 A032475 A032476 A032477 A032478 A032479 A032480 A032481 A032482 A032483 A032484 A032485

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (11): A032486 A032487 A032488 A032489 A032490 A032491 A032492 A032493 A032494 A032495 A032496 A032497

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (12): A032498 A032499 A032500 A032501 A032502 A032503 A032504 A032507 A046758 A050537 A050538 A050539

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (13): A050540 A050541 A050543 A050544 A050545 A050546 A050547 A050549 A050550 A050551 A050552 A050553

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (14): A050554 A050555 A050556 A050557 A050558 A050559 A050560 A050561 A050562 A050563 A050564 A050565

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (15): A050566 A050567 A050568 A050569 A050570 A050571 A050572 A050573 A050574 A050575 A050576 A050577

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (16): A050578 A050579 A050580 A050581 A050582 A050583 A050584 A050585 A050586 A050587 A050588 A050589

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (17): A050590 A050591 A050592 A050593 A050594 A050595 A050596 A050597 A050598 A050599 A050616 A050617

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (18): A050618 A050619 A050830 A050831 A050832 A050833 A050834 A050835 A050836 A050837 A050838 A050839

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (19): A050840 A050841 A050842 A050843 A050844 A050845 A050846 A050847 A050848 A050849 A050850 A050851

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (20): A050852 A050853 A050854 A050855 A050856 A050857 A050858 A050859 A050860 A050861 A050862 A050863

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (21): A050864 A050865 A050866 A050867 A050868 A050869 A050877 A050878 A050879 A050880 A050881 A050882

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (22): A050883 A050884 A050885 A050886 A050887 A050888 A050889 A050890 A050891 A050892 A050893 A050894

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (23): A050895 A050896 A050897 A050898 A050899 A050900 A050901 A050902 A050903 A050904 A050905 A050906

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (24): A050907 A050908 A053345 A053346 A053348 A053349 A053350 A053351 A053352 A053353 A053354 A053355

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (25): A053356 A053357 A053358 A053359 A053360 A053361 A053362 A053363 A053364 A053365 A053366

primes: values of n such that k*2^n-1 (or k*2^n+1) is prime, for k=1,3,5,7,... (26): A007505 A050522 A050523 A050524 A050525 A050526 A050527 A050528 A002255 A050413

Primes:: A005361, A002200, A002038, A006093, A007445, A007296, A001259, A006450, A001275

primeth recurrence: A007097*
primitive (1):: A000020, A003050, A002233, A002199, A000019, A005992, A001578, A006246, A006245, A002589
primitive (2):: A001122, A007348, A006248, A006991, A006039, A006036, A001913, A001123, A007627, A006576, A007349, A001124, A001125, A002975, A001126
Primitive factors, A002185, A007138, A002184
primitive polynomials: see also trinomials over GF(2)

primitive roots, sequences related to :

primitive roots, primes by: see primes by primitive root

primitive roots: A060749*, A001918*, A002199, A002229, A002230, A002231, A029932, A071894

primorial numbers, sequences related to :

primorial numbers: A002110*, A034386*

primorial numbers: see also A056113, A056129, A006862, A057588, A129912

primorial primes: A005234*, A014545*, A018239*, A006794*, A057704*, A057705*

principal character: A005368
prism numbers: A005914, A005915, A005919, A005920

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