[pggvusan] Another large, well understood prime number

What is the largest 1024-bit prime number for which P-1 has been completely recursively factored, i.e., recursive prime predecessor factorization notation? I submit 2^2^10-78^2+1 = 2^1024-6083 which has been deliberately constructed to permit a difference-of-squares algebraic factorization as the first step.

addprimes([1083494040106371332294227, 139064063171018168521503046101646577, 2841191921924985656661586344451800424539770776712116522717671893727359545610234669])

f(2^1024-6083) = (2(22(2)) ((()) ((2(2())))) (2(2) (()) (((2)))) (2(2) (()) ((((2))))) ((2() ()) ((2(()))) (222() () ())) ((2) (()) ((2)) (22((((2)))) (() (222)))) (((((2)))) (2() (() ())) (() () ((2) (() ())) (() () ((2))))) (2() () (()) (() () ((2) (2() () () (()) (2() (2) (222)))))) (22(2) (2(2() ())) ((()) (2() ()) (22(2) (() ()) (222(())) (22(2(())))))) (222(2() () () (2()) (() (()) (2() (2)) (() (2222222)) (2() (()) (()) (() ((2)))))) (() (()) (222) (2((2)) (((2)))) (22(22() (2) (2(2() ()))) (2(2()) (22(222)) (((2(()))) (22() (() ()))))))) (2((2)) (2(2) (2(())) (2(2())) (() (22() ())) (2((2)) (((2)))) (222() () (2) (2() ((()) (((22(2)))))))) (2() () (2(())) (() (2) (2()) (() (())) (22(2) (() ())) (() (2) (()) (()))) (() (() (2) (2) (2) (2() ()) (() (2())) ((2) (2) (() (2) (2) (2)) (((2() (() (2))) ((((2)) (() (2))))))))) (2() () (((2))) (2() ((2)) (((2))) (() (2)) (() ((2))) (22((2))) (2() (2) (2) (22(2)))) (2(2() (((2)))) (22((2) (() () () () () (2) (())))) (2(2) (2) (2) (22(2)) (() ((2)))))))) (() () (2) ((()) (222)) (22(2) (2) (222) (2(() (()))) (22((2(2(2())) ((2) (2())))) (() () () () (2) (() () (() (2())))))) (() (()) (2(2) (2)) (2222() () (22(2)) (() () () () (2()) ((222(()))) (222() (2()) (2() (((()) (222)))) (2() (() (2) (2) (()))))))) (22() (22(2(()))) (() ((22(2)) (() (())))) (2() (() (2() () ()) (22222())) (() (2) ((2)) (() () (() (2)) (22(2)) (() (()) (((2) (2()))))))) (() (2) (2() ((2)) ((2))) ((22(2222((2))) (() (() () (2) (2()))))) ((222) (22() ((()) (()) (2(2() () (() (())))))))) ((2) (()) (((2))) (22() (() () (()))) ((() (222) (() ()) (2() ()) (2222(2) (() (2)) (() (())) (2() (() (((2))))))) (((2) (22() (() ((2)) (222))) (() () (2) (() (() (() (2) (2))))) (2() (()) ((222(2() ((2)) (((2
time = 1min, 15,912 ms.
Pari/GP code

There are 6 offsets that are larger primes: -105, -179, -1397, -3177, -5025, -5409.

-105 has had previous work. However, p236-1 has one large prime factor 990139786733 and a remaining unfactored composite 18513940093499569750411376338999995867617006918696675688302638528027478760198817793813455365715959644984419056888960581140476054231587638951735401309894668051242387103404040341947341382002038055413925619981863105821613630700905060353967 , explored with GMP ECM until B1=5889420.