Symbolic prime generation for multiple-valued functions

The authors present new techniques based on the implicit representation and generation of primes for multiple-valued functions with sets of primes several orders of magnitude larger than existing methods. The key idea that makes this computation possible is the symbolic representation of multiple-valued cubes in a characteristic function form called the characteristic-cube function. This symbolic representation can be efficiently denoted using a binary decision diagram (BDD), which is known to be a very compact representation for Boolean formulas. Since there is no direct correspondence between the number of elements in a characteristic function and the size of the BDD representation that denotes it, very large sets of primes may be captured symbolically using the characteristic-cube function representation. Functions with other 10¹⁰ primes have been successfully generated by using the proposed method