  We consider cyclic unramified coverings of degree d of irreducible complex
smooth genus 2 curves and their corresponding Prym varieties. They provide
natural examples of polarized abelian varieties with automorphisms of order d.
The rich geometry of the associated Prym map, has been studied in several
papers, and the cases d=2, 3, 5, 7 are quite well-understood. Nevertheless,
very few is known for higher values of d. In this article we investigate if the
covering can be reconstructed from its Prym variety, that is, if the generic
Prym Torelli Theorem holds for these coverings. We prove this is so for the
so-called Sophie Germain prime numbers, that is, for $d\ge 11$ prime such that
$(d-1)/2$ is also prime. We use results of arithmetic nature on $GL_2$-type
abelian varieties combined with theta-duality techniques.
