素数原根的两个猜想

Two Conjecture for Primitive Root of Prime Number

应用计算机编程，对素数原根进行了研究，通过对100亿以下素数进行了验证，得出了两个猜想：（1）若P和q=4p＋1都是素数，则q的最小原根为2；（2）若p和q=2p＋1都是素数，当p=1（mod 4）时，2是q的最小原根，而当P=3（mod4）时，2不是q的最小原根。在验证这两个猜想的过程中，还发现对于P和2^kp＋1都为素数时，2不是2^k p＋1的最小原根（k〉2）。

The primitive root of prime number have been studied by application of computer programming. Two conjectures are obtained on basis of the verification on the prime numbers below 10 billion： （1） For any prime p and q, if q = 4 p ＋ 1 ,then 2 is the least primitive root of q. （2） For any prime p and q, q = 2 p ＋ 1 ,ifp = 1（med 4） ,then 2 is the least primitive root of q, if p = 3（reed 4）, then 2 is not the least primitive root of q. In the course of the verification on these two conje ctures, the autcor found that for any prime p and q, if q = 2kp ＋ 1, k 〉 2, then 2 is not the least primitive root of q.