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
A022012
Initial members of prime octuplets (p, p+2, p+6, p+12, p+14, p+20, p+24, p+26).
Original entry on oeis.org
17, 1277, 113147, 2580647, 20737877, 58208387, 73373537, 76170527, 100658627, 134764997, 137943347, 165531257, 171958667, 224008217, 252277007, 294536147, 309740987, 311725847, 364154027, 408936947, 515447747, 521481197, 528272177, 619010297, 626927447, 682809977
Offset: 1
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[p: p in PrimesUpTo(4*10^8) | forall{p+r: r in [2,6,12,14,20,24,26] | IsPrime(p+r)}]; // Vincenzo Librandi, Oct 01 2015
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Select[Prime[Range[2 10^9]], Union[PrimeQ[# + {2, 6, 12, 14, 20, 24, 26}]] == {True} &] (* Vincenzo Librandi, Oct 01 2015 *)
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forprime(p=2, 10^30, if (isprime(p+2) && isprime(p+6) && isprime(p+12) && isprime(p+14) && isprime(p+20) && isprime(p+24) && isprime(p+26), print1(p", "))) \\ Altug Alkan, Oct 01 2015
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use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2,6,12,14,20,24,26); # Dana Jacobsen, Sep 30 2015
A347848
Record gaps between prime octuplets of the form p + {0, 2, 6, 8, 12, 18, 20, 26} (initial members are A022011), divided by 210.
Original entry on oeis.org
75048, 323655, 422750, 2073918, 4243118, 5993757, 7828766, 11528083, 12215588, 15097361, 15513531, 17010400, 31025397, 44928642, 57138204, 75017391, 81443987, 97313005, 109587483, 110514347, 120045110, 120244355, 140472479, 140771332, 142099045, 265356757, 332391121
Offset: 1
a(1) = (A022011(2) - A022012(1))/210 = (15760091 - 11)/210 = 75048; 11 = A347849(1).
a(5) = (A022011(21) - A022011(20))/210 = (3734403131 - 2843348351)/210 = 424318, exceeding all previous differences; 2843348351 = A347849(5).
The primes at the lower end of the record gaps are given in
A347849.
A347852
Record gaps between prime octuplets of the form p + {0, 6, 8, 14, 18, 20, 24, 26} (initial members are A022013), divided by 210.
Original entry on oeis.org
933, 2719, 25782, 298074, 684607, 3152985, 3615775, 4062023, 9213717, 17131290, 18003995, 19350016, 23725387, 30570595, 34125949, 39157518, 61083539, 67660632, 83438975, 94515652, 117202015, 119103567, 126310893, 127678285, 144003855, 189879059, 197614054, 240073574
Offset: 1
a(1) = (A022013(2) - A022013(1))/210 = (284723 - 88793)/210 = 933; 88793 = A347853(1).
a(6) = (A022013(11) - A022013(10))/210 = (964669613 - 302542763)/210 = 3152985, exceeding all previous differences; 302542763 = A347853(6).
The primes at the lower end of the record gaps are given in
A347853.
Showing 1-4 of 4 results.
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