A347853
Primes at lower end of record gaps between prime octuplets given by A347852.
Original entry on oeis.org
88793, 284723, 1146773, 6560993, 74266253, 302542763, 3279413303, 4412997293, 11163865613, 42731353103, 67588200923, 90307985213, 108039383513, 253802571923, 378166268723, 508735164383, 912404760713, 1351905411533, 3353287304813, 4707449019173, 5993035649963, 7429168351463
Offset: 1
A022013
Initial members of prime octuplets (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26).
Original entry on oeis.org
88793, 284723, 855713, 1146773, 6560993, 69156533, 74266253, 218033723, 261672773, 302542763, 964669613, 1340301863, 1400533223, 1422475913, 1837160183, 1962038783, 2117861723, 2249363093, 2272018733, 2558211563
Offset: 1
- Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Matt C. Anderson)
- T. Forbes and Norman Luhn, Prime k-tuplets
- Stephan Ramon Garcia, Jeffrey Lagarias, and Ethan Simpson Lee, The error term in the truncated Perron formula for the logarithm of an L-function, arXiv:2206.01391 [math.NT], 2022.
- Norman Luhn and Hugo Pfoertner, 10 million terms of A022013, 7z compressed (47.9 MB) (2021).
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[p: p in PrimesUpTo(2*10^8) | forall{p+r: r in [6,8,14,18,20,24,26] | IsPrime(p+r)}]; // Vincenzo Librandi, Sep 30 2015
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Select[Prime[Range[200000]], Union[PrimeQ[# + {6, 8, 14, 18, 20, 24, 26}]] == {True} &] (* Vincenzo Librandi, Sep 30 2015 *)
Select[Prime[Range[125*10^6]],AllTrue[#+{6,8,14,18,20,24,26},PrimeQ]&] (* Harvey P. Dale, Jul 21 2025 *)
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forprime(p=2, 1e30, if (isprime(p+6) && isprime(p+8) && isprime(p+14) && isprime(p+18) && isprime(p+20) && isprime(p+24) && isprime(p+26) , print1(p", "))) \\ Altug Alkan, Sep 30 2015
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use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 6,8,14,18,20,24,26); # 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.
A347850
Record gaps between prime octuplets of the form p + {0, 2, 6, 12, 14, 20, 24, 26} (initial members are A022012), divided by 30.
Original entry on oeis.org
42, 3729, 82250, 605241, 1249017, 1734985, 1747606, 3550360, 9578800, 10562911, 12208504, 24101070, 26510262, 38121281, 38588851, 47884158, 50246371, 56392908, 59827439, 66233760, 114058040, 120197366, 141646351, 141808504, 153247005, 168751151, 235079194, 244505074
Offset: 1
a(1) = (A022012(2) - A022012(1))/30 = (1277 - 17)/30 = 42; 17 = A347851(1).
a(5) = (A022012(13) - A022012(12))/30 = (171958667 - 165531257)/30 = 214247, exceeding all previous differences; 1655531257 = A347851(5).
The primes at the lower end of the record gaps are given in
A347851.
Showing 1-4 of 4 results.
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