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Primes p such that p - 6 is a product of two consecutive primes.
1

%I #20 Oct 01 2013 17:58:04

%S 41,83,149,227,443,673,1153,1523,2027,4093,5189,6563,7393,9803,11027,

%T 12323,20717,39209,47059,50627,60497,64513,70753,95483,104933,123203,

%U 126733,131759,136897,154439,181457,186629,190093,194483,213449,233279,251003,256033

%N Primes p such that p - 6 is a product of two consecutive primes.

%C Is this sequence infinite?

%H K. D. Bajpai, <a href="/A098061/b098061.txt">Table of n, a(n) for n = 1..10000</a>

%e prime(3)*prime(4) = 35. 35+6 = 41, the first entry in the table.

%t f[n_]:=Prime[n]*Prime[n+1]+6; lst={}; Do[If[PrimeQ[f[n]],AppendTo[lst,f[n]]],{n,6!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2010 *)

%t Select[Times@@#+6&/@Partition[Prime[Range[100]],2,1],PrimeQ] (* _Harvey P. Dale_, Apr 25 2011 *)

%o (PARI) f(n,m) = for(x=2,n,z=(prime(x+1)*prime(x));if(isprime(z+m),print1(z+m",")))

%o (PARI) is(n)=if(n<9,return(0)); my(q=precprime(sqrtint(n-6))); n-6==q*nextprime(q+1) && isprime(n) \\ _Charles R Greathouse IV_, Jul 22 2013

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Sep 11 2004