A347851
Primes at lower end of record gaps between prime octuplets given by A347850.
Original entry on oeis.org
17, 1277, 113147, 2580647, 20737877, 171958667, 311725847, 408936947, 701679047, 1804302107, 4955335367, 7449267797, 14005112897, 22741837817, 52998494597, 61033681757, 74325366107, 78271296197, 90479441177, 218018750687, 236874793697, 560125662977, 657582657857
Offset: 1
A350828
Number of prime octuplets with initial member (A065706) between 10^(n-1) and 10^n.
Original entry on oeis.org
0, 2, 0, 1, 1, 3, 3, 9, 28, 136, 541, 2936
Offset: 1
a(1) = a(3) = 0 because there is no single-digit nor a 3-digit prime initial member of a prime octuplet.
a(2) = 2 because 11 and 17 are the only 2-digit members of A065706, i.e., primes to start a prime octuplet.
a(4) = a(5) = 1 because 1277 (resp. 88793) is the only prime with 4 (resp. 5) digits to start a prime octuplet.
Then there are a(6) = 3 six-digit primes, 113147, 284723 and 855713, which start a prime octuplet.
Cf.
A065706 (initial members p of prime octuplets (p, ..., p+26)),
A022011,
A022012,
A022013 (idem, specifically for each of the three possible patterns).
A375648
Products of prime 8-tuples (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26) where p = A022013(n).
Original entry on oeis.org
3868985835982814590518552822749329543261, 43207320984601757696213691690377119115644261, 287530494211069388143263747303929618940138523261, 2991325021830996455943969680355510324042937309261, 3433715221252595293789329211184553889095776281330363261, 523198428668721638888114210837839571392856841008842698982189261
Offset: 1
-
Map[Times @@ NextPrime[#, Range[0, 7]] &, Import["https://oeis.org/A022013/b022013.txt", "Data"][[;; 12, -1]]]
A145315
Numbers k for which the set {30*k-13, 30*k-11, 30*k-7, 30*k-1, 30*k+1, 30*k+7, 30*k+11, 30*k+13} forms a symmetrical prime octuplet.
Original entry on oeis.org
1, 43, 3772, 86022, 691263, 1940280, 2445785, 2539018, 3355288, 4492167, 4598112, 5517709, 5731956, 7466941, 8409234, 9817872, 10324700, 10390862, 12138468, 13631232, 17181592, 17382707, 17609073, 20633677, 20897582, 22760333, 23389302, 32968102, 36051016, 37215088
Offset: 1
-
spoQ[n_]:=Module[{c=30n},And@@PrimeQ[{c-13,c-11,c-7,c-1,c+1,c+7,c+11, c+13}]]; Select[Range[23000000],spoQ] (* Harvey P. Dale, Oct 10 2011 *)
Original entry on oeis.org
422, 1355, 4074, 5460, 31242, 329316, 353648, 1038255, 1246060, 1440679, 4593664, 6382389, 6669205, 6773694, 8748381, 9343041, 10085055, 10711252, 10819136, 12181959, 12804411, 13683806, 14044105, 15616253, 19232028, 20795482, 21014272, 25076295, 26366476, 27457318
Offset: 1
Cf.
A182393 (similar for type p + {0, 2, 6, 8, 12, 18, 20, 26}).
Cf.
A145315 (minus 1, similar for type p + {0, 2, 6, 12, 14, 20, 24, 26}).
A382285
Initial members of prime octuplets (p, p+4, p+12, p+24, p+28, p+40, p+48, p+52), where all primes are consecutive primes.
Original entry on oeis.org
241639, 44533249, 120833809, 245843149, 480454939, 547838359, 945331939, 1272712579, 1318911019, 1334157859, 1413122899, 1801178629, 1977960949, 2708995099, 3073533559, 3234255499, 3359304829, 3485412349, 3836960419, 4202567899, 4311168259, 4984840999, 5044981129
Offset: 1
-
list(lim) = {my(d0 = [4, 8, 12, 4, 12, 8, 4], s = vecsum(d0), d = vector(7, i, prime(i+1) - prime(i)), prv = 19); forprime(p = 23, lim, d = concat(vecextract(d, "^1"), p - prv); if(d == d0, print1(p - s, ", ")); prv = p);} \\ Amiram Eldar, Mar 21 2025
A382639
Initial members of prime 16-tuples containing two prime octuplets at minimum distance.
Original entry on oeis.org
10458834002271815117, 26476006821087640697, 44350865905809142637, 54014646858393564377, 62155369550078511587, 253586253591518370557, 304079924911990894547, 423291158347150012877, 511505988322414165037, 512761727903842750367, 644424770171034352457, 675759858713748355427
Offset: 1
- T. Forbes and Norman Luhn, Prime k-tuplets, Initial members of "L - consecutive prime k-tuplets with the smallest possible and constant gap (D)"
- Jörg Waldvogel and Peter Leikauf, Finding Clusters of Primes, I, Progress Report 2003 - 2005, Seminar for Applied Mathematics SAM Swiss Federal Institute of Technology ETH, CH-8092 Zürich (2003) (identifying first 94 terms).
- Jörg Waldvogel and Peter Leikauf, Parallelization of Low-Communication Processes, Seminar for Applied Mathematics SAM Swiss Federal Institute of Technology ETH, CH-8092 Zürich (alternate link).
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