Prime factorization: 1009 is prime. The exponent of prime number 1009 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1009 has exactly 2 factors. Factors of 1009: 1, 1009 Factor pairs: 1009 = 1 × 1009 1009 has no square factors that allow its square root to be ...
We have developed a framework to convert an arbitrary integer factorization problem to an executable Ising model by first writing it as an optimization function then transforming the k-bit coupling (k ≥ 3) terms to quadratic terms using ancillary variab
A Grouping Strategy Based on Prime Factorization for Capacitor Voltage Balancing of the Modular Multilevel ConverterThe Modular Multilevel Converter (MMC) is particularly attractive for medium and high power applications such as High-Voltage Direct Current (HVDC) systems. In order to reach a high ...
The modular multilevel converter (MMC) is attractive for high-power applications because of the advantages of its high modularity and high power quality. This paper proposes a prime factorization-based grouping strategy for capacitor voltage balancing of MMC. With prime factors arranged from the ...
Minor Prime Factorization for n-D Polynomial Matrices over Arbitrary Coefficient FieldSince z1 - f p z2, ⋯, zn ∣aij, where i = 1, 2, ... , m, j = 1, 2, ... , l, bij is independent of z1, and z1 - f p z2, ⋯, zn is a simple divisor of det F j1, j2, ...
FactorizationSemiprimeIn accordance with the distributive traits of semiprimes' divisors, the article proposes an approach that can find out the small divisor of a semiprime by parallel computing. The approach incorporates a deterministic search with a probabilistic search, requires less memory and can...
The optimal choice of chaotic maps is then used to apply the Chaotic Grey Wolf Optimizer (CGWO) to the problem of factoring a large semi prime into its prime factors. Assuming the number of digits of the factors to be equal, this is a computationally difficult task upon which the RSA-...
We construct a local unique factorization domain A such that the completion of A is T and such that the dimension of the formal fiber ring at every height one prime ideal of A is d - 1 and the dimension of the formal fiber ring of A at (0) is t.Fleming, Sarah M.Ji, LenaLoepp,...
The property that the prime factorization of large numbers is a challengingly difficult task is well utilized in RSA-based encryption algorithms. Due to the dominant application of the RSA public-key primitive in cryptography, the security of RSA has been extensively analyzed for various attack ...