A240596 Primes of the form p*q*r + 2 where p, q and r are consecutive primes.

107, 4201, 18181981, 29884303, 72147193, 81927499, 208506511, 383148631, 402473443, 1106558899, 1391119621, 1459314919, 1498299289, 1945171369, 4593570199, 7908301729, 8052037969, 9970592521, 10594343761, 11304695329, 14119758703, 15111907009, 23157107803

Offset: 1

Author

K. D. Bajpai, Apr 08 2014

Keywords

• nonn

Comments

All the terms in the sequence, except a(1), are congruent to 1 mod 6.

Examples

			107 is prime and appears in the sequence because 107 = (3*5*7)+2.
4201 is prime and appears in the sequence because 4201 = (13*17*19)+2.
		

Links

• K. D. Bajpai, Table of n, a(n) for n = 1..3525

Crossrefs

Cf. A000040, A048880, A051507.

Programs

Maple

KD := proc() local a, b; a:=ithprime(n)*ithprime(n+1)*ithprime(n+2); b:=a+2; if isprime(b) then RETURN (b); fi; end: seq(KD(), n=1..1000);

Mathematica

Select[Table[Prime[k]*Prime[k+1]*Prime[k+2]+2,{k,1,300}],PrimeQ]
Select[Times@@@Partition[Prime[Range[600]],3,1]+2,PrimeQ] (* Harvey P. Dale, Nov 21 2018 *)

PARI

s=[]; for(k=1, 1000, t=prime(k)*prime(k+1)*prime(k+2)+2; if(isprime(t), s=concat(s, t))); s \\ Colin Barker, Apr 09 2014