20120410, 05:03  #1 
Nov 2011
2^{2}×3 Posts 
Lucasian Criteria for the Primality of 2^n+3
Definition : Let be a number of the form :
Definition : Let's define starting seed as : Definition : Let's define sequence as : Conjecture : I have checked conjecture for all primes in this sequence with exponent below 200000 . Also , for there is no composite that satisfies relation from conjecture . Are there similar criteria in the literature for the numbers of this form ? 
20120410, 05:15  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×2,399 Posts 
[Stupid Question]
What if n mod 4 = 1? [/SQ] Also, the LL (and LLR) test(s) start with S_{0} and end with S_{i2}. Are you sure you meant S_{i1}, or did you mean S_{1}=S? 
20120410, 05:25  #3  
Nov 2011
14_{8} Posts 
Quote:
Yes , I mean : . Last fiddled with by princeps on 20120410 at 05:26 

20120410, 16:25  #4  
Nov 2003
1110001000000_{2} Posts 
Quote:
= 2*(2^n1 + 1). This test is just a disguised prp test working in the field GF((P_n)^2). The recursion is just a disguised way of performing exponentiation in this field. While the conjecture may be correct, (i.e. that the prp test is a true prime test) I do not know how to prove this. (nor, I suspect, does anyone else) 

20120410, 20:08  #5  
Nov 2003
2^{6}×113 Posts 
Quote:
P_n 1 ........... 

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