This is a PRP value of the Ramanujan Tau function.
http://dx.doi.org/10.1007/s11139-012-9420-8
http://www.wolframalpha.com/input/?i=RamanujanTau[41^28288]

3-PRP according to PFGW

Passed the Baillie-PSW primality test with Pari/GP, in 26h 04m.

To be completed...