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 ...
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, ...
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, ...
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 ...
Print.Test.Page.OK is a Windows software, which is compatible with Windows XP and all the later versions, including Windows 11. No matter which printer you have, you can print a sample page to verify ...
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, ...
Reports of a respiratory virus spreading in Wuhan, China, emerged in late 2019. After the number of cases outside China increased rapidly, the World Health Organization declared the novel coronavirus ...
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 ...
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