The period and numerals sum of repeating decimal

A prime p is said to be in a k-class if p is a prime divisor of 102k-1u+1,which leads to a classification for all primes.Let(b,10)=1 and the repetend of irreducible proper fraction a/b be q1q2…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 99(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.