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

1,1

Links

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A340307 A353249 A247114 * A142031 A302003 A094657

Adjacent sequences: A075586 A075587 A075588 * A075590 A075591 A075592

Keyword

nonn

Author

Amarnath Murthy, Sep 26 2002

Extensions

More terms from Matthew Conroy, Apr 30 2003

Status

approved