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We study a two-dimensional discrete directional maximal operator along theset of the prime numbers. We show existence of a set of vectors, which arelattice points in a sufficiently large annulus, for which the $\ell^2$ norm ofthe associated maximal operator with supremum taken over all large scales growswith an epsilon power in the number of vectors. This paper is a follow-up to aprior work on the discrete directional maximal operator along the integers bythe first and third author.

Directional maximal function along the primes