The expected constant in the Bateman-Horn conjecture is $$\frac1d \prod_p\frac{1-\frac{n_p}{p}}{1-\frac1p},$$ where $n_p$ is the number of roots of $f(x)$ modulo $p,$ and $d$ is the degree of $f(x).$ For the particular polynomial in question, this converges quite rapidly, and when the product is taken over the first 10000 primes, the constant is approximately $1.6235,$ which does not disagree with the experimental result.

For posterity, here is the Mathematica program:

f[x_] := 29160 x^3 + 30132 x^2 + 8046 x + 643
nn[p_] := Length[Solve[ff[x] == 0, x, Modulus -> p]]
rat[p_] := (1 - nn[p]/p)/(1 - 1/p)
bh[n_] := Product[rat[Prime[k]], {k,1,n}]/3

The expected constant in the Bateman-Horn conjecture is $$\frac1d \prod_p\frac{1-\frac{n_p}{p}}{1-\frac1p},$$ where $n_p$ is the number of roots of $f(x)$ modulo $p,$ and $d$ is the degree of $f(x).$ For the particular polynomial in question, this converges quite rapidly, and when the product is taken over the first 10000 primes, the constant is approximately $1.6235,$ which does not disagree with the experimental result.

For posterity, here is the Mathematica program:

f[x_] := 29160 x^3 + 30132 x^2 + 8046 x + 643
nn[p_] := Length[Solve[ff[x] == 0, x, Modulus -> p]]
rat[p_] := (1 - nn[p]/p)/(1 - 1/p)
bh[n_] := Product[rat[Prime[k]], {k,1,n}]/3