A127874 Prime numbers of the form (x^3)/2+(3x^2)/2+3x+3.

19, 71, 269, 379, 683, 883, 4663, 6949, 9883, 12239, 16433, 21491, 45631, 66403, 92683, 125119, 186733, 211051, 228383, 256121, 286019, 296479, 352619, 389483, 562589, 578971, 683983, 721619, 842759, 930619, 1150183, 1230391, 1372211

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn

Comments

Generating polynomial is Schur's polynomial of degree 3. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisible by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A127873.

Programs

Mathematica

a = {}; Do[If[PrimeQ[3 + 3 x + (3 x^2)/2 + x^3/2], AppendTo[a, 3 + 3 x + (3 x^2)/2 + x^3/2]], {x, 1, 300}]; a
Select[Table[x^3/2+(3x^2)/2+3x+3,{x,150}],PrimeQ] (* Harvey P. Dale, Apr 30 2018 *)