A075585 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 5.

19, 23, 37, 43, 97, 127, 223, 499, 673, 1213, 2309, 2729, 6089, 6269, 7589, 8969, 9239, 9281, 10709, 11549, 11969, 12539, 13397, 14321, 15329, 16829, 17489, 18059, 19139, 19379, 19469, 19889, 20747, 21317, 21839, 22109, 22619, 23369, 23561, 24179

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075586, A075587, A075588, A075589.

Programs

Magma

a:=[]; for k in PrimesInInterval(2,25000) 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 5 then  Append(~a,k); end if; end for; a; // Marius A. Burtea, Sep 26 2019

Mathematica

dpd5Q[p_]:=Length[Union[Flatten[FactorInteger[#][[All,1]]&/@Range[ p+1,NextPrime[ p]-1]]]]==5; Select[Prime[Range[3000]],dpd5Q] (* Harvey P. Dale, Aug 11 2021 *)

Extensions

More terms from Sam Alexander, Oct 21 2003