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A075585
Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 5.
10
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
1,1
LINKS
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 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 26 2002
EXTENSIONS
More terms from Sam Alexander, Oct 21 2003
STATUS
approved