A075583 Primes p such that the composite numbers between p and the next prime together contain exactly three distinct prime factors.

7, 29, 41, 59, 101, 137, 149, 179, 197, 227, 239, 269, 281, 311, 347, 521, 599, 617, 641, 809, 821, 827, 881, 1031, 1061, 1277, 1451, 1487, 1607, 1619, 1667, 1697, 1787, 1871, 1877, 1997, 2027, 2081, 2087, 2111, 2237, 2267, 2381, 2657, 2687, 2711, 2801, 2999

Offset: 1

Author

Amarnath Murthy, Sep 26 2002

Keywords

• nonn

Comments

p+2 is prime for all members p except 7. - David Wasserman, Jan 20 2005

Links

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

Crossrefs

Cf. A052297, A075580, A059960, A075584, A075585, A075586, A075587, A075588, A075589.

See A080899 for another version.

Programs

Magma

a:=[]; for k in PrimesInInterval(2,3000) 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 3 then  Append(~a,k); end if; end for; a; // Marius A. Burtea, Sep 26 2019

Extensions

More terms from David Wasserman, Jan 20 2005