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 A075588 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 8. 10
 73, 83, 131, 167, 173, 251, 331, 383, 443, 563, 643, 739, 971, 1123, 1223, 1367, 1579, 1609, 1783, 1867, 1999, 2293, 2539, 2617, 2683, 3083, 3217, 3253, 3343, 3457, 3847, 4003, 4513, 4783, 4813, 4969, 5167, 5233, 5527, 5737, 5779, 5839, 5857, 6199, 6733 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE For p = 131, the next prime number is 137. The numbers between 131 and 137 and the prime factors are respectively 132 { 2, 3, 11 }, 133 { 7, 19 }, 134 { 2, 67 }, 135 { 3, 5 }, 136 { 2, 17 }. The set of prime divisors is { 2, 3, 5, 7, 11, 17, 19, 67 } and has 8 elements, so 131 is term. - Marius A. Burtea, Sep 26 2019 MATHEMATICA Select[Partition[Prime[Range[1000]], 2, 1], Length[Union[ Flatten[ FactorInteger[ Range[ #[[1]]+1, #[[2]]-1]], 1][[All, 1]]]]==8&][[All, 1]] (* Harvey P. Dale, Dec 26 2019 *) PROG (MAGMA) a:=[]; for p in PrimesInInterval(2, 7000) do b:={}; for s in [p..NextPrime(p)-1] do if not IsPrime(s) then b:=b join Set(PrimeDivisors(s)); end if; end for; if #Set(b) eq 8 then Append(~a, p); end if; end for; a; // Marius A. Burtea, Sep 26 2019 CROSSREFS Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075586, A075587, A075589. Sequence in context: A260555 A064667 A217237 * A039483 A104998 A033247 Adjacent sequences:  A075585 A075586 A075587 * A075589 A075590 A075591 KEYWORD nonn AUTHOR Amarnath Murthy, Sep 26 2002 EXTENSIONS More terms from Matthew Conroy, Apr 30 2003 STATUS approved

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Last modified September 25 00:48 EDT 2020. Contains 337333 sequences. (Running on oeis4.)