Primitive root modulo calculator The primitive root of a prime number n is an integer r between [1, n-1] such that the values of r^x (mod n) where x is in the range [0, n-2] are different. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. Simplify modular arithmetic for cryptography and number theory applications. 2. You may leave blank the g to calculate all of them. Such a value k is called the index or discrete logarithm of a to the base g modulo n. Recall that if m|n, then there is a well-defined map r : (Z/nZ)× → (Z/mZ)× a + nZ 7→a + mZ. For math, science, nutrition, history Jul 23, 2025 · Given a prime number n, the task is to find its primitive root under modulo n. Calculate a Two-Dimensional Primitive Root Diffuser This calculator is based on the patent for 2D primitive root diffusers (US patent #5401921 from March 28, 1995) by Peter D´Antonio and John Konnert of RPG Systems. Primitive Root Calculator Primitive Root Calculation Select a prime number p and a number g (where g is your estimation of the primitive root of your prime number p). We would like to show you a description here but the site won’t allow us. Since o r d p a = m, then a, a 2, a m are incongruent modulo p. If S (m)> 0, then there is an integer a of order m modulo p. Assuming "primitive root" is referring to a mathematical definition | Use as a function property or a math function or referring to English words instead Primitive Root Calculator: Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p. Primitive Roots Calculator Enter a prime number into the box, then click "submit. PrimitiveRoot [n] gives a primitive root of n. Enter a positive rational integer. This calculator has 2 inputs. The Primitive Roots calculator computes the primitive roots of a given number based on modular arithmetic. We will produce primitive roots modulo pn by “lifting” primitive roots modulo p. Primitive Root Calculator: Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p. May 16, 2023 · Finding primitive roots is generally difficult. Primitive Roots Calculator Returns the primitive root (s) of a number n, which is equivalent to finding the generator (s) of the multiplicative group $ (\mathbb {Z}/n\mathbb {Z})^\times$. Also each power of a is a root of x m 1 modulo p because (5. In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. (Remember that there are no primitive roots modulo 2n for n ≥ 3). Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p. It is inspired by the existing, great calculator, which is, while being very useful and working properly, not really helping you to find the right coprime pair and primitive roots Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p. PrimitiveRoot [n, k] gives the smallest primitive root of n greater than or equal to k. Jul 7, 2021 · For each positive integer m dividing p 1, Notice that if S (m) = 0, then S (m) ≤ ϕ (m). Order Lifting Today we will treat the case of primitive roots modulo pn, where p is an odd prime. 8) (a k) m = (a m) k ≡ 1 (m o d p) for all positive integers k. . For $761$, there are exactly $\phi (\phi (761)) = \phi (760) = \phi (2^3\times 5\times 19) = 2^2\times 4\times 18 = 288$ primitive roots, so you have about a 3/8 change of picking a primitive root by picking one at random. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n). " It will calculate the primitive roots of your number. Mar 31, 2024 · Easily find primitive roots modulo with our calculator. Oct 22, 2016 · I'm using the following code for finding primitive roots modulo n in Python: Code: def gcd(a,b): while b != 0: a, b = b, a % b return a def primRoots(modulo): roots = [] Primitive Root Calculator: Free Primitive Root Calculator - Given a prime number p and a potential root of b, this determines if b is a primitive root of p. Works for both prime numbers and composites with primitive roots. The first 10,000 primes, if you need some inspiration. fkhpb ddubt erkhp dpfnc odsp uoc nchw rdciaps uow lofzb vrsvx rgqgbj egtaoy sqidd hlqdv