I found a paper here: http://eprint.iacr.org/2009/008.pdf which generalizes a result from Lenstra's and Pomerance's paper.

The paper is "A note on Agrawal conjecture" by Roman Popovych.

Here is the abstract:

We prove that Lenstra proposition suggesting existence of many counterexamples to Agrawal
conjecture is true in a more general case. At the same time we obtain a strictly ascending chain of subgroups of the group (Zp[X]/(Cr(X)))* and state the modified conjecture that the set {X-1, X+2} generate big enough subgroup of this group.

Here is the url for a paper from a student scientific conference containing some numerical results:

http://www.fmph.uniba.sk/fileadmin/user_upload/editors/studium/svk/2009/INF/vana.pdf.