2. if the periodicity of 1/n is n-1 then n must be prime. the converse is not true.

3. if the periodicity of 1/p is always a factor of p-1.

4. if the periodicity of 1/p is p-1 then it must exhibit the property of revolution. hence a revolution characteristic can be associated to the prime number p.

5. on the basis of periodicity of reciprocals of prime numbers, they may be classified as true primes and pseudo-primes. (total-reciprocal-periodic prime (trp) or partial-reciprocal-periodic prime (prp))

6. the periodicity of 1/p

^{2}is p*(periodicity of 1/p). In fact the periodicity of 1/n

^{2}is either n*(periodicity of 1/n) or LCM of n and periodicity of 1/n.

7. the perodicity of 1/(p

_{1}*p

_{2}) is the LCM of the perodicities of 1/p

_{1}and 1/p

_{2}.

8. if the decimal part (including left zeroes) of 1/n is denoted by d, then the decimal part of 1/d is n preceded by [d]-[n] zeroes. ([ ] signifies number of digits)

9. the location of nulls in a discontinuous revolution characteristic may be symmetrical or asymmetrical. (Symmetrically discontinuous or Asymmetrically discontinuous)

10. the diameter of circular revolution of a number the length of whose reciprocal is d is always d/2.

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how the function value of n* on that no. is obtained? it is not the position the revolution is starting from.what is that?

ReplyDeletehttp://en.wikipedia.org/wiki/Long_prime

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