摘要
如果素数p是102k-1u+1的一个因子,则说p在一k-类中,由此导出一个对素数的分类.设(b,10)=1且既约真分数a/b的循环节是q1q2…q2s,那么qi+qs+i=9当且仅当b的所有素因子都属于一k-类,这时a/b的数码和为9s.既约真分数a/3n+2的数码和为9(t-1)/2+r,这里t是a/3n+2的周期,r是a模9的最小非负剩余.如果1/p的周期等于p-1或(p-1)/2,那么p是一个素数.
A prime p is said to be in a k - class if p is a prime divisor of 10^2k-1u ＋ 1, which leads to a classification for all primes. Let （ b, 10） = 1 and the repetend of irreducible proper fraction a/b be q1 q2^… q2s, then qi ＋ qs ＋ i = 9 if and only if all prime divisors of b belong to one k-class, the numerals sum of a/b is 9s in this case. The numerals sum of irreducible proper fraction a/3n＋2 is 9（ t - 1）/2 ＋ r,where t is the period of a/3n＋2 and r is the least non-negative residue of a modulo 9. If the period of 1/p equal to p - 1 or （ p - 1 ）/2, then p is a prime.
出处
《云南大学学报（自然科学版）》
CAS
CSCD
北大核心
2007年第3期217-222,共6页
Journal of Yunnan University(Natural Sciences Edition)
基金
The Natural Science Foundation of Hunan Province(05JJ30141).
关键词
循环小数
周期
数码和
素数
repeating decimal
period
numerals sum
prime
