A127882 Primes of the form 60*(x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1).

163, 977611, 12294697, 37985853397, 49252877161, 137434331779, 830329719061, 1626105882361, 8060524420261, 11467771684597, 13008402510163, 15315610041211, 43633838254429, 71635442712061, 125119099806661

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn

Comments

Generating polynomial is Schur's polynomial of 5-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, A127879, A127880, A127881, A127883.

Programs

GAP

Filtered(List([1..2000],x->60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1)),IsPrime); # Muniru A Asiru, Apr 30 2018

Maple

select(isprime,[seq(60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1),x=1..2000)]); # Muniru A Asiru, Apr 30 2018

Mathematica

a = {}; Do[If[PrimeQ[60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2], AppendTo[a, 60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2]], {x, 1, 1000}]; a