prime sequences A080050/A080051

[Ralf Stephan]

Can someone prove there is a mapping between

%N A080050 Primes p such that 2^p-1 and the p-th Fibonacci number have a common
 factor. Prime members of A074776.
and
%N A080051 Common factors of 2^p-1 and the p-th Fibonacci number, p prime.
?
Define p the former, gcd the latter numbers.

gcd = 8k(p-1)+9 ???
x is the position of the twin prime pair.
All shown gcd are prime.

Thanks,
ralf

p      gcd      estim.(gcd-9)/(8p) please verify
-------------------
11     89       1
8501   680081   10
10867  260809   3
13109  3146161  30
14633  1170641  10
15401  123209   1
17657  423769   3
19211  153689   1
19541  156329   1
22481  179849   1
24359  779489   4
25243  403889   2
26111  208889   1
29411  235289   1
30851  246809   1
34961  279689   1
36007  864169   3
42443  2376809  7
43331  346649   1
45523  728369   2
46187  1108489  3
46601  372809   1
47591  380729   1
50411  403289   1
57251  458009   1
58027  1392649  3
61001  488009   1
62921  503369   1
63131  505049   1
64123
70639
74293
76919
78941
81761
87583
91099
92333
94841
94903
95257
95651
101021
101203
102551
102673
108461
113933
116411
117361x
117371
121021
123551
127331
129581 1036649 1
132403 2118449 2
134951 1079609 1
136511 1092089 1
144461 1155689 1
153191 1225529 1
156371 1250969 1
157901 1263209 1
161233 6449321 5
164683 19761961 
168851 1350809 
174613 2793809 
176537 4236889 
177761 1422089 
181957 4366969