A240715 Primes p such that p*q*r + 6 and p*q*r - 6 are primes where q and r are the next two primes after p.

569, 1531, 1549, 7103, 7451, 9013, 10627, 10853, 11779, 11783, 12671, 12941, 14821, 14851, 17489, 18493, 20717, 20959, 25237, 26309, 27739, 29669, 29873, 34549, 35977, 36251, 37591, 38351, 38639, 39551, 40129, 45589, 46957, 47317, 48781, 55163, 55259

Offset: 1

Author

K. D. Bajpai, Apr 10 2014

Keywords

• nonn

Examples

			569 is in the sequence because 569*571*577 + 6 = 187466729 and 569*571*577 - 6 = 187466717 are both prime where 571 and 577 are the next two primes after 569.
1531 is in the sequence because 1531*1543*1549 + 6 = 3659253823 and 1531*1543*1549 - 6 = 3659253811 are both prime where 1543 and 1549 are the next two primes after 1531.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..1444

Crossrefs

Cf. A006094, A048880, A051507, A240596.

Programs

Magma

[p: p in PrimesUpTo(10^5) | IsPrime(t-6) and IsPrime(t+6) where t is p*NextPrime(p)*NextPrime(NextPrime(p))]; // Bruno Berselli, Apr 11 2014

Maple

KD := proc(n) local a,b,d; a:=ithprime(n)*ithprime(n+1)*ithprime(n+2); b:=a+6; d:=a-6; if  isprime(b) and isprime(d) then RETURN (ithprime(n)); fi; end: seq(KD(n), n=1..10000);

Mathematica

c = 0; Do[If[PrimeQ[Prime[n]*Prime[n+1]*Prime[n+2] +6] && PrimeQ[Prime[n]*Prime[n+1]*Prime[n+2] -6],c=c+1;Print[c, " ", Prime[n]]],{n,1,500000}];
KD={};   f=Prime[n+1]*Prime[n+2];  Do[p=Prime[n]; If[ PrimeQ[p*f+6] && PrimeQ[p*f-6], AppendTo[KD,p]], {n,10000}]; KD
Select[Partition[Prime[Range[6000]],3,1],AllTrue[Times@@#+{6,-6},PrimeQ]&][[All,1]] (* Harvey P. Dale, Oct 29 2022 *)