Quote:
Originally Posted by efeuvete
I did not count numbers 1 and 2, that's all; 83284 with them, Ok.

1 is not a prime number, so your count is still one off.
You are probably skipping 2 and 5 based on your description. If so, then ok.
Your method seems to play with the properties of the
Pisano periods. For some primes (see details on that Wiki page), the period will divide p1, and consequently you will have F(p1)=F(0)=0 (mod p), and for others, you will have F(p+1)=F(0)=0 (mod p). So, indeed, for the first rule, there shouldn't be false negative results other than 2 and 5.
Your pseudo's are probably numbers with low Pisano periods (including some Lucas numbers?), but I haven't looked in detail.