I found a 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.