A075589 Primes p such that the number of distinct prime divisors of all composite numbers between p and the next prime is 9.

89, 151, 233, 257, 263, 271, 353, 367, 373, 503, 541, 571, 587, 601, 647, 653, 727, 733, 751, 977, 991, 1013, 1181, 1291, 1321, 1433, 1453, 1621, 1753, 1861, 2281, 2371, 2377, 2671, 3061, 3079, 3203, 3323, 3793, 4051, 4073, 4283, 4357, 4519, 4591, 4639

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A052297, A075581, A075580, A059960, A075583, A075584, A075585, A075586, A075587, A075588.

Programs

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

Extensions

More terms from Matthew Conroy, Apr 30 2003