Displaying 1-10 of 26 results found.
Initial members of prime septuplets.
+10
29
11, 5639, 88799, 165701, 284729, 626609, 855719, 1068701, 1146779, 6560999, 7540439, 8573429, 11900501, 15760091, 17843459, 18504371, 19089599, 21036131, 24001709, 25658441, 39431921, 42981929, 43534019, 45002591, 67816361, 69156539, 74266259, 79208399, 80427029, 84104549, 86818211, 87988709, 93625991, 124066079
CROSSREFS
Initial members of all of the first prime k-tuplets:
Cf. A343637 (distance from 10^n to the next septuplet).
Initial members of prime 9-tuplets (or nonuplets).
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28
7, 11, 13, 17, 1277, 88789, 113143, 113147, 855709, 74266249, 182403491, 226449521, 252277007, 408936947, 521481197, 626927443, 910935911, 964669609, 1042090781, 1116452627, 1209950867, 1422475909, 1459270271, 1645175087, 2117861719, 2335215973, 2558211559, 2843348351, 2873599429, 2966003057, 3447123283, 3947480417
COMMENTS
Primes prime(m) such that prime(m+8) = prime(m) + 30. - Zak Seidov, Jul 06 2015
MATHEMATICA
{p, q, r, s, t, u, v, w, x} = Prime@ Range@ 9; lst = {}; While[p < 1000000001, If[p + 30 == x, AppendTo[lst, p]; Print@ p]; {p, q, r, s, t, u, v, w, x} = {q, r, s, t, u, v, w, x, NextPrime@ x}]; lst (* Robert G. Wilson v, Jul 06 2015 *) Select[Partition[Prime[Range[5 10^6]], 9, 1], #[[1]]+30==#[[9]]&][[;; , 1]] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Jul 01 2024 *)
PROG
(PARI) main(size)=v=vector(size); i=0; m=1; while(i<size, if(prime(m)+30===prime(m+8), v[i++]=prime(m)); m++; ); v \\ Anders Hellström, Jul 08 2015 (Magma) [NthPrime(n): n in [0..2*10^4] | NthPrime(n+8) eq (NthPrime(n) + 30)]; // Vincenzo Librandi, Jul 08 2015
CROSSREFS
Initial members of all of the first prime k-tuplets:
Initial members of prime 10-tuplets (or decaplets).
+10
28
11, 9853497737, 21956291867, 22741837817, 33081664151, 83122625471, 164444511587, 179590045487, 217999764107, 231255798857, 242360943257, 294920291201, 573459229151, 663903555851, 666413245007, 688697679401, 696391309697, 730121110331, 867132039857, 974275568237, 976136848847, 1002263588297
CROSSREFS
Initial members of all of the first prime k-tuplets:
Initial members of prime 11-tuples.
+10
28
11, 1418575498573, 2118274828903, 4396774576273, 6368171154193, 6953798916913, 7908189600581, 10527733922591, 12640876669691, 27899359258003, 28138953913303, 34460918582323, 38545620633251, 40362095929003, 42023308245613, 43564522846961, 44058461657443, 60268613366231, 60596839933361, 61062361183903, 71431649320301
COMMENTS
It appears that this lists only starting primes for one of the A083409(11) = 2 constellations with minimal diameter A008407(11) = 36, i.e., the union of A213646 and A213647, while there are other prime 11-tuples with larger diameter. - M. F. Hasler, Dec 03 2018
CROSSREFS
Initial members of all of the first prime k-tuples:
Initial members of prime 12-tuplets.
+10
27
11, 1418575498567, 27899359257997, 34460918582317, 76075560855367, 186460616596327, 218021188549237, 234280497145537, 282854319391717, 345120905374087, 346117552180627, 380284918609481, 437163765888581, 604439135284057, 701889794782061, 727417501795057, 980125031081081, 1041814617748747, 1090754719898917, 1277156391416021, 1487854607298791
CROSSREFS
Initial members of all of the first prime k-tuplets:
Initial members of prime 13-tuplets.
+10
27
11, 13, 10527733922579, 186460616596321, 1707898733581273, 3266590043460823, 4289907938811613, 4422879865247923, 5693002600430263, 7582919852522851, 7697168877290909, 7933248530182091, 10071192314217869, 10907318641689703, 11987120084474369, 15991086371740199, 20475715985020181, 21817283854511261, 21817283854511263, 22443709342850669, 28561589689237439, 31979851757518501
CROSSREFS
Initial members of all of the first prime k-tuplets:
Numbers n such that n, n+4, n+6, n+10, n+16, n+18, n+24, n+28, n+30, n+34, n+40, n+46 and n+48 are all prime.
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27
13, 4289907938811613, 5693002600430263, 21817283854511263, 48290946353555023, 51165618791484133, 53094081535451893, 70219878257874463, 98633358468021313, 99142644093930373, 104814760374339133, 166784569423739203, 167841416726358493, 184601252515266523, 263331429949004353, 272039012072134243, 339094624362619243, 363319822006646623, 363760043662280383, 437335541550793003, 455289126169953193
COMMENTS
All terms after the first == 1483 (mod 2730).
n+4, n+16, n+28, n+46 are in A001359. (End)
LINKS
Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..944 [first 21 terms from Vladimir Vlesycit, first 99 terms from Matt C. Anderson]
PROG
(PARI) is(n)=isp=isprime; isp(n) && isp(n+4) && isp(n+6) && isp(n+10) && isp(n+16) && isp(n+18) && isp(n+24) && isp(n+28) && isp(n+30) && isp(n+34) && isp(n+40) && isp(n+46) && isp(n+48) \\ Anders Hellström, Sep 05 2015 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**16, 4, 6, 10, 16, 18, 24, 28, 30, 34, 40, 46, 48); # Dana Jacobsen, Oct 07 2015
CROSSREFS
Initial members of all of the first prime k-tuplets:
Numbers n such that n, n+4, n+6, n+10, n+16, n+18, n+24, n+28, n+30, n+34, n+36, n+46 and n+48 are all prime.
+10
27
1707898733581273, 3266590043460823, 4422879865247923, 10907318641689703, 32472302129057023, 52590359764282573, 60229684381540753, 67893346321234513, 93179596929433093, 115458868925574253, 140563537593599353, 142977538681261363, 148877505784397623, 166362638531783773, 232442516762530153, 236585787518684683, 255933372890105143, 317294052871840123, 325853825645632363, 337188071215909993, 344447962857168403
LINKS
Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..802 [first 21 terms from Vladimir Vlesycit, first 90 terms from Matt C. Anderson]
PROG
(PARI) Q=isprime;
isok(n) = Q(n) && Q(n+4) && Q(n+6) && Q(n+10) && Q(n+16) && Q(n+18) && Q(n+24) && Q(n+28) && Q(n+30) && Q(n+34) && Q(n+36) && Q(n+46) && Q(n+48); \\ Michel Marcus, Aug 04 2015 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**16, 4, 6, 10, 16, 18, 24, 28, 30, 34, 36, 46, 48); # Dana Jacobsen, Oct 09 2015
CROSSREFS
Initial members of all of the first prime k-tuplets:
Numbers n such that n, n+2, n+6, n+8, n+12, n+18, n+20, n+26, n+30, n+32, n+36, n+42 and n+48 are all prime.
+10
27
11, 7933248530182091, 20475715985020181, 21817283854511261, 33502273017038711, 40257009922154141, 49242777550551701, 49600456951571411, 75093141517810301, 84653373093824651, 119308586807395871, 129037438367672951, 129706953139869221, 151242381725881331, 158947009165390331, 161216594737343261, 167317340088093311, 176587730173540571, 178444395317213141, 197053322268438521, 301854920123441801
LINKS
Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..817 [first 21 terms from Vladimir Vlesycit, first 98 terms from Matt C. Anderson]
PROG
(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**16, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48); # Dana Jacobsen, Oct 10 2015
CROSSREFS
Initial members of all of the first prime k-tuplets:
Numbers n such that n, n+2, n+8, n+14, n+18, n+20, n+24, n+30, n+32, n+38, n+42, n+44 and n+48 are all prime.
+10
27
7697168877290909, 10071192314217869, 11987120084474369, 28561589689237439, 62321320746357689, 73698766709402669, 75046774774314359, 79287805466244209, 98551408299919409, 136720189890477209, 225735856757596019, 234065221633327919, 302834818301440259, 360345440708336099, 385443070970192069, 387494664213890249, 466256026285842809, 539043082132918379, 570108181108560929, 610147978081735109
LINKS
Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..1036 [first 20 terms from Vladimir Vlesycit; first 104 terms from Matt C. Anderson]
PROG
(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**16, 2, 8, 14, 18, 20, 24, 30, 32, 38, 42, 44, 48); # Dana Jacobsen, Oct 13 2015
CROSSREFS
Initial members of all of the first prime k-tuplets:
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