Prime Numbers Quiz

<p>Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes</p> Signup and view all the answers

<p>Primality</p> Signup and view all the answers

<p>Trial division = Checks whether n is a multiple of any integer between 2 and $\sqrt{n}$ Miller-Rabin primality test = Fast but has a small chance of error AKS primality test = Always produces the correct answer in polynomial time but is too slow to be practical Mersenne numbers = Numbers for which particularly fast primality testing methods are available</p> Signup and view all the answers

<p>Prime number = A natural number greater than 1 that is not a product of two smaller natural numbers Composite number = A natural number greater than 1 that is not prime Primality = The property of being prime Fundamental theorem of arithmetic = Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order</p> Signup and view all the answers

<p>5 = Prime 4 = Composite 24,862,048 = Mersenne prime 2 = Prime</p> Signup and view all the answers

<p>Number divisible only by 1 or itself = Prime number A product (2 × 2) in which both numbers are smaller than 4 = Composite number Natural number greater than 1 that is not prime = Composite number Number for which particularly fast primality testing methods are available = Mersenne numbers</p> Signup and view all the answers

<p>5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself = 5 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4 = 4 The largest known prime number as of December 2018 is a Mersenne prime with 24,862,048 decimal digits = 24,862,048 Every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order = Fundamental theorem of arithmetic</p> Signup and view all the answers