It is well known that when using the Miller–Rabin primality test for 64-bit integers, we only need to test with the base set $\{2, 325, 9375, 28178, 450775, 9780504, 1795265022\}$ to ensure ...

Department of Civil Engineering, Gamal Abdel Nasser University of Conakry, Conakry, Guinea. Multiplication tables are well known for their elementary role in mathematics education. But as structured ...

ABSTRACT: This paper systematically studies the properties of multiplication tables through three fundamental operations: ΣT , ΔT , ΠT . We show how these operations reveal deep arithmetic structures, ...

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Abstract: With the increasing popularity and usage of cryptography and network security, prime generation and primality testing has become a significant issue. Various primality tests have been ...

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below is the code for finding the smallest r, that the order of n modulo r is bigger than log^2(n). Order of n modulo r is the smallest integer k that satisfies n^k = 1 mod r. And we need to find the ...

The online computer game “Is this prime?” tests a player’s knowledge of prime numbers—and just surpassed 2,999,999 attempts. Give it a whirl. The Greek mathematician Euclid may very well have proved, ...

Determining whether a given integer is prime or composite is a basic task in number theory. We present a primality test based on quantum order finding and the converse of Fermat's theorem. For an ...