On the least prime primitive root modulo a prime
نویسندگان
چکیده
منابع مشابه
On the least prime primitive root modulo a prime
We derive a conditional formula for the natural density E(q) of prime numbers p having its least prime primitive root equal to q, and compare theoretical results with the numerical evidence. 1. Theoretical result concerning the density of primes with a given least prime primitive root Let us denote, following Elliott and Murata [4], by g(p) and G(p) the least primitive and the least prime primi...
متن کاملLeast primitive root of prime numbers
Let p be a prime number. Fermat's little theorem [1] states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between 1 and p-1. A primitive root [1] of p is a number r such that any integer a between 1 and p-1 can be expressed by a=r^k mod p, with k a nonnegative integer smaller that p-1. If p is an odd prime number then r is a primitive root of p if and only if r^((p-...
متن کاملThe Least Prime Primitive Root and the Shifted Sieve
If p is a prime, we define g(p) to be the least prime that is a primitive root (mod p), and similarly for prime powers p. The problem of establishing a bound for g(p) uniformly in p is quite difficult, comparable with establishing a uniform upper bound for the least prime in an arithmetic progression. Indeed, there do not exist any uniform upper bounds for g(p) that improve upon the current bou...
متن کاملUniform Bounds for the Least Almost-prime Primitive Root
A recurring theme in number theory is that multiplicative and additive properties of integers are more or less independent of each other, the classical result in this vein being Dirichlet’s theorem on primes in arithmetic progressions. Since the set of primitive roots to a given modulus is a union of arithmetic progressions, it is natural to study the distribution of prime primitive roots. Resu...
متن کاملA new prime p for which the least primitive root (modp) and the least primitive root (modp2) are not equal
With the aid of a computer network we have performed a search for primes p < 1012 and revealed a new prime p = 6692367337 for which its least primitive root (mod p) and its least primitive root (mod p2) are not equal.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2002
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-02-01370-4