On a property of superposition of the generating functions   ln(1/(1-F(x)))
  Obtained a new property of superposition of the generating functions ln(1/(1-F(x))), where F(x) - generating function with integer coefficients, which allows the construction a primality tests. The theorem which is based on compositions of positive numbers and its corollary are proved. Examples are given. Key words: Generating functions, superposition of generating functions, composition of a natural number. 
Dmitry Kruchinin
math.CO math.NT