Thread: Odd Fibonacci pseudoprimes View Single Post 2013-05-25, 23:01 #3 efeuvete   "Fernando Villanueva" May 2013 Madrid /Spain 5 Posts I did not count numbers 1 and 2, that's all; 83284 with them, Ok. As far as I've checked (Up to 1.066.393), from the first rule there are not false negatives. I'm afraid my triple test is not very fast but in any case, I have no idea of what can be considered fast testing primes. I will describe the two first rules now. My short english and spanish time, (01h00) don't allow me going to the third one now. If it is worth I'll Try to do that tomorrow. Here I go: Lets define a function to be applied on numbers ending 1,3,7 or 9. I will call it SH() (From shift) SH (N) = N-1 (N, Natural number N ending on 1 or 9) SH (N) = N+1 (N, Natural number N ending on 3 or 7) And Lets Call F(N) to the N term of Fibonacci sequence FIRST RULE: IF F(SH(N)) MOD N = 0 then N is prime or pseudo as to 1st rule (167 pseudos) SECOND RULE Lets call S to the set of all numbers which satisfy FIRST RULE. If N belongs to S and F(N) belongs to S too, N is prime as to 1st and 2nd rules (83 pseudos) In order to test FIRST RULE you must consider that when you divide the Fibonacci sequence for a number N, the remainders sequence satisfy the same fibonacci rule F(N+1)=F(N)+F(N-1) And in order to test second rule you need a nice trick a bit complicated to write now, I'll do if it is worth while. Thanks, Last fiddled with by efeuvete on 2013-05-25 at 23:28 Reason: Fibonacci rule  