(2^1127239+2^563620+1)/5 is 3-PRP, originally found using LLR ver. 3.7.0, as a part of an effort to prove that 2^1203793-2^601897+1 is 37-th Gaussian Mersenne norm.
This is a Fermat PRP at base 3, 7, 5, 11, 13, 17, 101 and 137 - using PFGW ver. 1.2.0 for Windows.
11-PRP test performed by Ken Davis
137-PRP test performed by Paul Underwood
Additionally Paul Underwood has reported this:
Primality testing (2^1127239+2^563620+1)/5 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1127239+2^563620+1)/5 is Lucas PRP! (112247.5827s+0.0020s)
To be completed...