A347849
Primes at lower end of record gaps between prime octuplets given by A347848.
Original entry on oeis.org
11, 25658441, 93625991, 226449521, 2843348351, 4090833821, 13421076281, 18856092371, 26092031081, 54270148391, 66449431661, 111422173391, 124168028051, 280837571081, 875319936761, 1247050623431, 3589081520021, 6363702282011, 7479508339601, 10804857261041, 15199582184861
Offset: 1
A022011
Initial members of prime octuplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26).
Original entry on oeis.org
11, 15760091, 25658441, 93625991, 182403491, 226449521, 661972301, 910935911, 1042090781, 1071322781, 1170221861, 1394025161, 1459270271, 1712750771, 1742638811, 1935587651, 2048038451, 2397437501, 2799645461
Offset: 1
- Martin Gardner, The Last Recreations, Chapter 12: Strong Laws of Small Primes, Springer-Verlag, 1997, pp. 191-205, especially p. 197.
- Martin Gardner, Patterns in primes are a clue to the strong law of small numbers, Mathematical Games column, Scientific American, (December, 1980), pp. 20ff.
- 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 A022011, 7z compressed (47.7 MB) (2021).
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[p: p in PrimesUpTo(4*10^8) | forall{p+r: r in [2,6,8,12,18,20,26] | IsPrime(p+r)}]; // Vincenzo Librandi, Oct 01 2015
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Select[Prime[Range[2 10^9]], Union[PrimeQ[# + {2, 6, 8, 12, 18, 20, 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+8) && isprime(p+12) && isprime(p+18) && isprime(p+20) && isprime(p+26), print1(p", "))) \\ Altug Alkan, Oct 01 2015
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use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2,6,8,12,18,20,26); # Dana Jacobsen, Sep 30 2015
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.
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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