prime factorizations of important sequences: see factorizations of important sequences
prime factors of n, number of A001222
prime numbers of measurement: A002048 *, A002049 *
prime numbers: A000040 *, A008578
prime plus twice a square: A046903
prime powers: A000961 *, A025475 * (excludes primes)
prime pyramid: A051237 *, A036440
Prime quadruplets:: A007530
Prime races:: A007351 , A007355 , A007354 , A007353 , A007352 , A007350
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(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
PRIMEGAME: A007542 , A007546 , A007547
PrimePi(x), number of primes <= x: A000720 *
primes , sequences related to (start):
primes : A000040 *
primes gaps, see primes, gaps between
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 , (start):
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 (start): (**) means the divergence occurs beyond the last entry shown in the database. [Indexed by Patrick De Geest (pdg(AT)worldofnumbers.com)]
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 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: 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 (start):
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, consecutive, A006549 , A007700 , A007513 , A007529 , A007530 , A006489
primes, cuban: A002407 , A002648 , A007645
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, Fermat: A019434 *, A050922
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 (start):
primes, gaps between, A001223 *, A007921 *, A030173 *, A037201 , A023200
primes, gaps between, A001359 , A006512 , A077800 , A001097 , A049591 , A124582 -A124596
primes, gaps between, A031924 A031925 A031926 A031927 A031928 A031929 A031930 A031931 A031932 A031933 A031934 A031935 A031936 A031937 A031938 A031939
primes, gaps between, records for: A000101 * (upper end), A002386 * (lower end), A005250 * (gaps)
primes, gaps between, see also: A005669 , A002540 , A000230 , A000232 , A001549 , A001632
primes, gaps between, see also: primes, differences between
primes, Germain: see primes, Sophie Germain
primes, good: A046869 , A028388
primes, half-quartan: A002646
primes, happy: A035497
primes, Higgs: A007459
primes, home, see also A048985 , A064841
primes, home: A037274 * (base 10), A048986 * and A064795 (base 2)
primes, Honaker: A033548
primes, iccanobiF: A036797
primes, in arithmetic progressions, sequences related to (start):
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 cojecture), 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