The least primitive root in number fields
نویسندگان
چکیده
منابع مشابه
A 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.
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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...
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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...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2004
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa115-3-8