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 A075586 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 6. 10
 31, 47, 67, 103, 109, 163, 193, 277, 313, 349, 379, 397, 457, 463, 487, 877, 1087, 1093, 1279, 1303, 1567, 1873, 2269, 2347, 2473, 2797, 3697, 4447, 4789, 4999, 5077, 5413, 5503, 5923, 6007, 6217, 6469, 6997, 7603, 7639, 7723, 7933, 8779, 9277, 10159 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For very large n, the probability of a(n) not being a twin prime is extremely small, unless the twin primes conjecture is false. - Sam Alexander, Oct 20 2003 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE Between 31 and the next prime 37, there are 5 composite numbers whose prime divisors are respectively for 32: {2}, 33: {3,11}, 34: {2,17}, 35: {5,7} and 36: {2,3}; hence, these distinct prime divisors are {2,3,5,7,11,17}, the number of these distinct prime divisors is 6, so 31 is a term. - Bernard Schott, Sep 26 2019 MATHEMATICA Select[Partition[Prime[Range[1250]], 2, 1], Length[Union[Flatten[ FactorInteger/@ Range[ #[[1]]+1, #[[2]]-1], 1][[All, 1]]]]==6&][[All, 1]] (* Harvey P. Dale, May 25 2020 *) PROG (MAGMA) a:=[]; for k in PrimesInInterval(2, 10000) do b:={}; for s in [k..NextPrime(k)-1] do if not IsPrime(s) then b:=b join Set(PrimeDivisors(s)); end if; end for; if #Set(b) eq 6 then  Append(~a, k); end if; end for; a; // Marius A. Burtea, Sep 26 2019 CROSSREFS Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075587, A075588, A075589. Sequence in context: A130096 A229624 A270781 * A033221 A127576 A139896 Adjacent sequences:  A075583 A075584 A075585 * A075587 A075588 A075589 KEYWORD nonn AUTHOR Amarnath Murthy, Sep 26 2002 EXTENSIONS More terms from Sam Alexander, Oct 20 2003 STATUS approved

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Last modified September 18 23:30 EDT 2020. Contains 337175 sequences. (Running on oeis4.)