> - Long ago ;-) I made some investigations about the period of inverse of
> prime numbers (1/p) (Is this good English ?).
> I found an empiric relation between the number of digits of the period
> (d) et the fact that p is prime, namely that d is a divisor of p-1. I
> have been told that this was proved by Gauss. Is there a Web page about
> this ? Is this could be of any use in the search for large primes ?
The number of digits in the period is whatever power of 10 you need to make 1
mod p. If 10 is a primitive root of p, then the period is p-1. Ex.
1/7=.(142857), 1/17=.(0588235294117647).
16, of course, is not a primitive root of anything, so reciprocals never have
full period in base 16, and most of them have odd period.
phma
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