A127879 Primes of the form x^4 + 4*x^3 + 12*x^2 + 24*x + 24.

3760073, 9853769, 117051593, 181145609, 2517933833, 8999750153, 10486376969, 20852229449, 26640445193, 56713997513, 65555973569, 136653695753, 172008443273, 262819256009, 330127243553, 340704528713, 362619554249

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn

Comments

Generating polynomial is Schur's polynomial of 4-degree. 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

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A127873, A127874, A127875, A127876, A127877, A127878, A127880, A127881, A127882, A127883.

Programs

GAP

Filtered(List([1..2000],x->x^4+4*x^3+12*x^2+24*x+24),IsPrime); # Muniru A Asiru, Apr 30 2018

Maple

select(isprime,[seq(x^4+4*x^3+12*x^2+24*x+24,x=1..2000)]); # Muniru A Asiru, Apr 30 2018

Mathematica

a = {}; Do[If[PrimeQ[24 + 24 x + 12 x^2 + 4 x^3 + x^4], AppendTo[a, 24 + 24 x + 12 x^2 + 4 x^3 + x^4]], {x, 1, 1000}]; a
Select[Table[x^4+4x^3+12x^2+24x+24,{x,780}],PrimeQ[#]&] (* Harvey P. Dale, Jan 24 2013 *)