Found with PFGW Version 3.7.5

240^6953-6953^240 is 2-PRP! (9.3772s+0.0018s)
240^6953-6953^240 is 3-PRP! (9.0083s+0.0019s)
240^6953-6953^240 is 5-PRP! (9.8026s+0.0021s)
240^6953-6953^240 is 7-PRP! (8.7590s+0.0018s)
240^6953-6953^240 is 11-PRP! (9.2361s+0.0016s)

Primality testing 240^6953-6953^240 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 19
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N+1 BLS with factored part 0.06% and helper 0.01% (0.20% proof)
240^6953-6953^240 is Fermat and Lucas PRP! (49.3601s+0.0046s)

To be completed...