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%I #21 Sep 08 2022 08:45:07
%S 89,151,233,257,263,271,353,367,373,503,541,571,587,601,647,653,727,
%T 733,751,977,991,1013,1181,1291,1321,1433,1453,1621,1753,1861,2281,
%U 2371,2377,2671,3061,3079,3203,3323,3793,4051,4073,4283,4357,4519,4591,4639
%N Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 9.
%H Amiram Eldar, <a href="/A075589/b075589.txt">Table of n, a(n) for n = 1..10000</a>
%e For p = 233, the next prime number is 239. The numbers between 233 and 237 and the prime divisors are respectively 234 {2, 3, 13}, 235 {5, 47}, 236 {2, 59}, 237 {3, 79 }, 238 {2, 7, 17}. The set of prime divisors is {2, 3, 5, 7, 13, 17, 47, 59, 79} and has 9 elements, so 233 is a term.
%o (Magma) a:=[]; for p in PrimesInInterval(2,5000) 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 9 then Append(~a,p); end if; end for; a; // _Marius A. Burtea_, Sep 26 2019
%Y Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075586, A075587, A075588.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Sep 26 2002
%E More terms from _Matthew Conroy_, Apr 30 2003
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