A144953 Primes of form n^3 + 2.

2, 3, 29, 127, 24391, 91127, 250049, 274627, 328511, 357913, 571789, 1157627, 1442899, 1860869, 2146691, 2924209, 3581579, 5000213, 5177719, 6751271, 9129331, 9938377, 10503461, 12326393, 14348909, 14706127, 15438251, 18191449

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Sep 26 2008

Keywords

• nonn
• easy

Comments

The Hardy-Littlewood conjecture K (p. 51) suggests that this sequence is infinite and gives an asymptotic estimate for the density of this sequence. - Charles R Greathouse IV, Jul 06 2010

Links

• Vincenzo Librandi and Robert Israel, Table of n, a(n) for n = 1..10000 (first 2900 terms from Vincenzo Librandi)
• G. H. Hardy and J. E. Littlewood, Some problems of 'Partitio numerorum'; III: On the expression of a number as a sum of primes, Acta Math., Vol. 44, No. 1 (1923), pp. 1-70.

Crossrefs

Cf. A067200.

Programs

Magma

[a: n in [0..800] | IsPrime(a) where a is n^3+2]; // Vincenzo Librandi, Nov 30 2011

Maple

N:= 10000: # number of terms desired
R[1]:= 2: count:= 1:
for n from 1 by 2 while count < N do
   p:= n^3+2;
   if isprime(p) then
     count:= count+1;
     R[count]:= p;
   end if
end do:
seq(R[n],n=1..N); # Robert Israel, Jan 29 2013

Mathematica

lst={};Do[s=n^3;If[PrimeQ[p=s+2],AppendTo[lst,p]],{n,6!}];lst
A144953={2};Do[If[PrimeQ[p=n^3+2],AppendTo[A144953,p]],{n,1,10^5,2}];A144953 (* Zak Seidov, Nov 05 2008 *)
Select[Table[n^3+2,{n,0,7000}],PrimeQ] (* Vincenzo Librandi, Nov 30 2011 *)

PARI

for(n=0,1e3,if(isprime(k=n^3+2),print1(k","))) \\ Charles R Greathouse IV, Jul 06 2010

Formula

a(n) = A067200(n)^3 + 2. - Zak Seidov, Sep 16 2013

Extensions

a(1)=2 from Zak Seidov, Nov 05 2008

Reference and index correction from Charles R Greathouse IV, Jul 06 2010