4^n-3 status

[paulunderwood]

In May of 2001, Andy Steward, provided the following N^2-1 factorisation of 4^n-3 to the Yahoo group primeform:

Expo Len N^2-1 %
2 2 100.00%
3 2 100.00%
5 4 100.00%
6 4 100.00%
7 5 100.00%
10 7 100.00%
11 7 100.00%
12 8 100.00%
47 29 100.00%
58 35 100.00%
61 37 100.00%
75 46 100.00%
87 53 100.00%
133 81 100.00%
168 102 100.00%
226 137 100.00%
347 209 100.00%
425 256 100.00%
868 523 62.54%
1977 1,191 21.72%
2815 1,695 29.69%
3378 2,034 13.72%
4385 2,641 15.65%

The sequence continues:
4^5286-3
2^7057-3[*]
4^7200-3
4^8230-3
4^8340-3
4^13175-3
4^17226-3
4^18276-3
4^25237-3
4^33211-3
4^58463-3
4^59662-3
4^94555-3
4^120502-3
4^177473-3
4^197017-3
[*] was proven by Preda Mihailescu with his Cycloprove program in 1999.

Please can you provide updated N^2-1 factoriztion percentages for these numbers -- a lot work has been done on the Cunningham tables since 2001.

Note: N-1=4[4^(n-1)-1] and N+1=2[2^(2n-1)-1].

[paulunderwood]

http://perta.fizyka.amu.edu.pl/pnq/ is a good source, but I don't know if Wojciech Florek is making the best of the resources such as Cunningham tables, factoring programs and primailty proving programs. If you has the time you could help him

(No longer unanswered )