A007530 -id:A007530 - cp's OEIS frontend

A257127 Initial members of prime 10-tuplets (or decaplets).

11, 9853497737, 21956291867, 22741837817, 33081664151, 83122625471, 164444511587, 179590045487, 217999764107, 231255798857, 242360943257, 294920291201, 573459229151, 663903555851, 666413245007, 688697679401, 696391309697, 730121110331, 867132039857, 974275568237, 976136848847, 1002263588297

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

M. F. Hasler, Table of n, a(n) for n = 1..10000 (first 101 terms from Tim Johannes Ohrtmann), Mar 01 2022
Tony Forbes and Norman Luhn Prime k-tuplets
Norman Luhn, The big database of "The smallest prime k-tuplets", section "10-tuplets": up to 10^20 as of March 2022.

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime quintuplets: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: this sequence out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

A257129 Initial members of prime 11-tuples.

Original entry on oeis.org

11, 1418575498573, 2118274828903, 4396774576273, 6368171154193, 6953798916913, 7908189600581, 10527733922591, 12640876669691, 27899359258003, 28138953913303, 34460918582323, 38545620633251, 40362095929003, 42023308245613, 43564522846961, 44058461657443, 60268613366231, 60596839933361, 61062361183903, 71431649320301

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

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

Tim Johannes Ohrtmann and Dana Jacobsen, Table of n, a(n) for n = 1..13723 [This replaces an earlier b-file from Tim Johannes Ohrtmann]
Tony Forbes k-tuplets

Initial members of all of the first prime k-tuples:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruples: A007530.
prime quintuples: A086140 out of A022007, A022006.
prime sextuples: A022008.
prime septuples: A257124 out of A022009, A022010.
prime octuples: A065706 out of A022011, A022012, A022013.
prime nonuples: A257125 out of A022547, A022548, A022545, A022546.
prime 10-tuples: A257127 out of A027569, A027570.
prime 11-tuples: this sequence out of A213646, A213647.
prime 12-tuples: A257131 out of A213601, A213645.
prime 13-tuples: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuples: A257166 out of A257167, A257168.
prime 15-tuples: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuples: A257308 out of A257369, A257370.
prime 17-tuples: A257373 out of A257374, A257375, A257376, A257377.

A257131 Initial members of prime 12-tuplets.

Original entry on oeis.org

11, 1418575498567, 27899359257997, 34460918582317, 76075560855367, 186460616596327, 218021188549237, 234280497145537, 282854319391717, 345120905374087, 346117552180627, 380284918609481, 437163765888581, 604439135284057, 701889794782061, 727417501795057, 980125031081081, 1041814617748747, 1090754719898917, 1277156391416021, 1487854607298791

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

Tim Johannes Ohrtmann and Dana Jacobsen, Table of n, a(n) for n = 1..5759 [This replaces an earlier b-file from Tim Johannes Ohrtmann]
Tony Forbes k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: this sequence out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

A257135 Initial members of prime 13-tuplets.

Original entry on oeis.org

11, 13, 10527733922579, 186460616596321, 1707898733581273, 3266590043460823, 4289907938811613, 4422879865247923, 5693002600430263, 7582919852522851, 7697168877290909, 7933248530182091, 10071192314217869, 10907318641689703, 11987120084474369, 15991086371740199, 20475715985020181, 21817283854511261, 21817283854511263, 22443709342850669, 28561589689237439, 31979851757518501

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

Norman Luhn, Table of n, a(n) for n = 1..30259 (terms 1..54 from Tim Johannes Ohrtmann, terms 55..5256 from Dana Jacobsen)
Tony Forbes and Norman Luhn, k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: this sequence out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

A257137 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.

Original entry on oeis.org

13, 4289907938811613, 5693002600430263, 21817283854511263, 48290946353555023, 51165618791484133, 53094081535451893, 70219878257874463, 98633358468021313, 99142644093930373, 104814760374339133, 166784569423739203, 167841416726358493, 184601252515266523, 263331429949004353, 272039012072134243, 339094624362619243, 363319822006646623, 363760043662280383, 437335541550793003, 455289126169953193

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

From Robert Israel, Aug 27 2015: (Start)
All terms after the first == 1483 (mod 2730).
n+4, n+16, n+28, n+46 are in A001359. (End)

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]
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
Norman Luhn, Table of n, a(n) for n = 1..6305

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, this sequence, A257138, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

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

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

A257138 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.

Original entry on oeis.org

1707898733581273, 3266590043460823, 4422879865247923, 10907318641689703, 32472302129057023, 52590359764282573, 60229684381540753, 67893346321234513, 93179596929433093, 115458868925574253, 140563537593599353, 142977538681261363, 148877505784397623, 166362638531783773, 232442516762530153, 236585787518684683, 255933372890105143, 317294052871840123, 325853825645632363, 337188071215909993, 344447962857168403

Offset: 1

Tim Johannes Ohrtmann, Apr 16 2015

nonn

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]
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
Norman Luhn, Table of n, a(n) for n = 1..5290

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, this sequence, A257139, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

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

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

a(18) corrected by Matt C. Anderson, Aug 03 2015

A257139 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.

Original entry on oeis.org

11, 7933248530182091, 20475715985020181, 21817283854511261, 33502273017038711, 40257009922154141, 49242777550551701, 49600456951571411, 75093141517810301, 84653373093824651, 119308586807395871, 129037438367672951, 129706953139869221, 151242381725881331, 158947009165390331, 161216594737343261, 167317340088093311, 176587730173540571, 178444395317213141, 197053322268438521, 301854920123441801

Offset: 1

Tim Johannes Ohrtmann, Apr 17 2015

nonn

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]
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
Norman Luhn, Table of n, a(n) for n = 1..5000

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, this sequence, A257140, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

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

A257140 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.

Original entry on oeis.org

7697168877290909, 10071192314217869, 11987120084474369, 28561589689237439, 62321320746357689, 73698766709402669, 75046774774314359, 79287805466244209, 98551408299919409, 136720189890477209, 225735856757596019, 234065221633327919, 302834818301440259, 360345440708336099, 385443070970192069, 387494664213890249, 466256026285842809, 539043082132918379, 570108181108560929, 610147978081735109

Offset: 1

Tim Johannes Ohrtmann, Apr 17 2015

nonn

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]
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
Norman Luhn, Table of n, a(n) for n = 1..6264

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, this sequence, A257141.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

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

A257141 Numbers n such that n, n+2, n+12, n+14, n+18, n+20, n+24, n+30, n+32, n+38, n+42, n+44 and n+48 are all prime.

Original entry on oeis.org

10527733922579, 15991086371740199, 22443709342850669, 69759046409087909, 94415460183744419, 164873121596539229, 197053322268438509, 212971209388223159, 215768926871613989, 248170682800139819, 270109976153617319, 326374793491266239, 341896216415143109, 341987213500572359, 362035072661912369, 401062754451879239, 441180406661470349, 450928996714672349, 503035098004929209, 533306698691196149

Offset: 1

Tim Johannes Ohrtmann, Apr 17 2015

nonn

Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, Table of n, a(n) for n = 1..803 [first 20 terms from Vladimir Vlesycit, first 86 terms from Matt C. Anderson]
Tony Forbes and Norman Luhn, Smallest Prime k-tuplets
Norman Luhn, Table of n, a(n) for n = 1..5307 (Zip file)

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, this sequence.
prime 14-tuplets: A257166 out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

isok(n)={isp=isprime;isp(n) &&isp(n+2)&&isp(n+12) &&isp(n+14) &&isp(n+18)&&isp(n+20)&&isp(n+24) &&isp(n+30) &&isp(n+32) &&isp(n+38) &&isp(n+42)&&isp(n+44)&&isp(n+48)} \\ Anders Hellström, Sep 05 2015

use ntheory ":all"; say for sieve_prime_cluster(1, 10**15, 2,12,14,18,20,24,30,32,38,42,44,48); # Dana Jacobsen, Oct 13 2015

A257166 Initial members of prime 14-tuplets.

Original entry on oeis.org

11, 21817283854511261, 79287805466244209, 841262446570150721, 1006587882969594041, 2682372491413700201, 2714623996387988519, 5009128141636113611, 5012524663381750349, 6120794469172998449, 6195991854028811669, 6232932509314786109, 6808488664768715759, 7126352574372296381, 7993822923596334941, 10756418345074847279, 11319107721272355839

Offset: 1

Tim Johannes Ohrtmann, Apr 17 2015

nonn

Norman Luhn, Table of n, a(n) for n = 1..1810 (up to 10^22) (terms 1..394 from Tim Johannes Ohrtmann and Dana Jacobsen)
Tony Forbes and Norman Luhn, k-tuplets

Initial members of all of the first prime k-tuplets:
twin primes: A001359.
prime triples: A007529 out of A022004, A022005.
prime quadruplets: A007530.
prime 5-tuples: A086140 out of A022007, A022006.
prime sextuplets: A022008.
prime septuplets: A257124 out of A022009, A022010.
prime octuplets: A065706 out of A022011, A022012, A022013.
prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.
prime decaplets: A257127 out of A027569, A027570.
prime 11-tuplets: A257129 out of A213646, A213647.
prime 12-tuplets: A257131 out of A213601, A213645.
prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
prime 14-tuplets: this sequence out of A257167, A257168.
prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
prime 16-tuplets: A257308 out of A257369, A257370.
prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

cat b25716[78].txt | perl -nE '/(\d+)$/; $r{$1}++; END { say ++$i," $" for sort {$a<=>$b} keys %r }' # [Given the b-files from the two 14-tuple sequences] _Dana Jacobsen, Oct 18 2015

cp's OEIS Frontend

A257127 Initial members of prime 10-tuplets (or decaplets).

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A257129 Initial members of prime 11-tuples.

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A257131 Initial members of prime 12-tuplets.

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A257135 Initial members of prime 13-tuplets.

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A257137 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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A257138 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.

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A257139 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.

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A257140 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.

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A257141 Numbers n such that n, n+2, n+12, n+14, n+18, n+20, n+24, n+30, n+32, n+38, n+42, n+44 and n+48 are all prime.

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PARI

Perl

A257166 Initial members of prime 14-tuplets.

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Perl