Phi_168860L(10)/337721/19250041
http://factordb.com/index.php?id=1100000000777139998
http://stdkmd.com/nrr/repunit/prpfactors.htm
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$ ./pfgw64 -tc -q"((10^8443-10^4222+2)*(10^8443+1)^3+(10^4222-2)*(10^16886+10^8443)-1)/23020547704922501"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]

Primality testing ((10^8443-10^4222+2)*(10^8443+1)^3+(10^4222-2)*(10^16886+10^8443)-1)/23020547704922501 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N+1 test using discriminant 23, base 1+sqrt(23)
Calling N-1 BLS with factored part 0.04% and helper 0.00% (0.13% proof)
((10^8443-10^4222+2)*(10^8443+1)^3+(10^4222-2)*(10^16886+10^8443)-1)/23020547704922501 is Fermat and Lucas PRP! (117.0704s+0.0033s)
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To be completed...