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A289250 Primes p such that p + 4 is a semiprime. 2

%I #7 Jul 02 2017 02:33:47

%S 2,5,11,17,29,31,47,53,61,73,83,89,107,137,139,151,157,173,179,181,

%T 197,199,211,233,263,283,317,331,337,367,373,389,409,433,443,449,467,

%U 523,541,547,569,577,587,593,607,619,631,677,683,691,709,719,727,733,751,787,809,811,827

%N Primes p such that p + 4 is a semiprime.

%C Except for case p=5, p+4 is never a perfect square.

%C For p = {2, 11, 31, 73, 139, 433, 1759, 2017} p+4 is a product of two consecutive primes.

%H Charles R Greathouse IV, <a href="/A289250/b289250.txt">Table of n, a(n) for n = 1..10000</a>

%e 2+4=6=2*3, 5+4=9=3*3, 11+4=15=3*5 (all semiprimes).

%t Select[Prime@ Range@ 150, PrimeOmega[# + 4] == 2 &] (* _Michael De Vlieger_, Jun 29 2017 *)

%o (PARI) issemi(n)=bigomega(n)==2

%o is(n)=isprime(n) && issemi(n+4) \\ _Charles R Greathouse IV_, Jul 02 2017

%Y Cf. A001358, A063637, A082919, A241484,

%K nonn

%O 1,1

%A _Zak Seidov_, Jun 29 2017

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