families of elliptic curves, arXiv:0708.4042, primes of form 4*(a^3) + 27*(b^3)

[Jonathan Post]

Tony Noe has done great work on OEIS about primes in quadratic forms.
There's a particularly important cubic form in this new paper, for
which I've done a quick prime search "by hand":

arXiv:0708.4042
    Title: Moments of the critical values of families of elliptic
curves, with applications
    Authors: Matthew P. Young
    Comments: 24 pages
    Subjects: Number Theory (math.NT)
    We make conjectures on the moments of the central values of the
family of all elliptic curves and on the moments of the first
derivative of the central values of a large family of positive rank
curves. In both cases the order of magnitude is the same as that of
the moments of the central values of an orthogonal family of
L-functions. Notably, we predict that the critical values of all rank
1 elliptic curves is logarithmically larger than the rank 1 curves in
the positive rank family.
    Furthermore, as arithmetical applications we make a conjecture on
the distribution of a_p's amongst all rank 2 elliptic curves, and also
show how the Riemann hypothesis can be deduced from sufficient
knowledge of the first moment of the positive rank family (based on an
idea of Iwaniec).

Prop 2.2 of the paper, p.8 of 24, begins:

Suppose 4a^3 + 27b^3 is squarefree...

First I made by hand a table, restricting to positive a,b, circling
the squarefree.

Then I picked out the primes of the form 4*(a^3) + 27*(b^3) for
positive a,b which I think begins:

31, 43, 127, 223, 283, 733, 811, 829, 1051, 1129, 1213, 1471, ...
but is not in OEIS.

Is this correct?  Perhaps Tony or someone wants to do the easy coding
and extending, in preparation for the end of OEIS/njas vacation?

Again, "primes of the form xxx" are usually uninteresting, but this is
about deep truths in Elliptic Curve theory.