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Old 2005-11-01, 09:27   #1
paulunderwood
 
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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].
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Old 2006-03-21, 23:46   #2
paulunderwood
 
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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

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