OFFSET
1,1
COMMENTS
The polynomials are cyclotomic(7,x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6, cyclotomic(9,x) = 1 + x^3 + x^6, cyclotomic(14,x) = 1 - x + x^2 - x^3 + x^4 - x^5 + x^6, and cyclotomic(18,x) = 1 - x^3 + x^6. The numbers 7, 9, 14 and 18 are in the sixth row of A032447.
By Schinzel's hypothesis H, there are an infinite number of n that yield simultaneous primes. Note that the two first-degree cyclotomic polynomials, x-1 and x+1, yield the twin primes for the numbers in A014574.
REFERENCES
See A087277.
MATHEMATICA
t = {}; n = 0; While[Length[t] < 30, n++; If[PrimeQ[Cyclotomic[7, n]] && PrimeQ[Cyclotomic[9, n]] && PrimeQ[Cyclotomic[14, n]] && PrimeQ[Cyclotomic[18, n]], AppendTo[t, n]]]; t
Select[Range[251*10^5], AllTrue[Cyclotomic[{7, 9, 14, 18}, #], PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 29 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Dec 11 2013
STATUS
approved