20060722, 16:12  #1 
Nov 2004
UK
2·19 Posts 
Proth Test Limits
I'm a little confused by Proth's Theorem (http://mathworld.wolfram.com/ProthsTheorem.html)...
If I were to write a function which performed a proth test given the pair of values n, and k; how would I know when to stop iterating through values for a. As I understand it, there appears to a 50% chance that any given 'a' value will work. However, say I write a function that iterates a from 1 to 1000, surely there is a chance, albeit a small chance) that none of those values will work, although a number > 1000 ~may~ work. Is there a hard limit for a, or should I be looking at the percentages  after all 10 values for a would give me a very high percentage chance of at least one of the working? 
20060723, 18:29  #2  
Nov 2003
2^{2}·5·373 Posts 
Quote:
in the size of the number bering tested. The result is due to Burgess. If GRH is true, than a much smaller limit can be proved: 2 log^2 N. The constant 2 is due to E. Bach. 

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