Number Theory

    

Periodic Tables of Prime Numbers

Authors: George Plousos

When we divide any integer n by a prime number p on a base B of the arithmetic system, we get a decimal extension that has a constant period length, which is equal to λ. For many values ​​of n we get the same period of p but from another digit. p has exactly r=(p-1)/λ different periods. So we need to test many values ​​of n to find all the periods of p. However, we can easily locate and manage all periods of p if we know the values ​​of two numbers, b and λ, because then we can construct a table that allows easy access to any digit of any period of p. To do this we use the relationship (x, y) = b^(rx + y) mod p. This relationship gives the position (x, y) of the table an integer value n such that the n/p fraction forms the y-th period of p from the x-th digit.

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[v1] 2020-05-05 11:26:03

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