PPT-Design and Analysis of Prime Number Sieves

Seth Futrell Matthew Ritchie Dakota Perryman Mark Thompson Tags Tots Background History Prime numbers have fascinated the human race for millennia with solutions to finding primes predating the times of euclid Primes continue to amaze mathematicians and theoretical thinkers daily Research of these fascinating numbers continues in present day with the continuing growth of the field of number theory and encryption protocols . By Matt Anderson. 4/9/2011. Prime numbers are integers that are divisible by only 1 and themselves.. P. ={primes} = {2,3,5,7,11,…}. There are an infinite number of prime numbers.. Let . π. (x) be the prime counting function. . Presented by Alex Atkins. What’s a Prime?. An integer p >= 2 is a prime if its only positive integer divisors are 1 and p. . Euclid proved that there are infinitely many primes. . The primary role of primes in number theory is stated in the Fundamental Theory of Arithmetic, which states that every integer n >= 2 is either a prime or can be expressed as a product of a primes.. History, theories and applications. By Kim . Wojtowicz. Definition of a Prime Number. A Prime number is a number that has exactly 2 Distinct factors: itself and 1. . Smallest prime number is 2, it is also the only even prime number.. Remember to Silence Your Cell . Phone and Put It In Your Bag!. Definition of Prime and Composite Numbers. A natural number that has exactly two distinct (positive) factors is called a . prime. . number. Learning Goals. We will use our divisibility rules so that we can decompose numbers into prime factors.. We’ll know we understand when we can identify the prime factors that are used to form a number.. Number Theoretic Transform and Its Inverse. . Note. ：. (. 1) . M. is a . prime number. , (mod . M. ): . 是指除以 . M. . 的餘數. (2) . N. is a factor of . M. −1. . (Note: when . Daniel . FreemaN. , SLU. Old school codes. Full knowledge of the code is needed to both encrypt messages. and to decrypt messages.. The code can only be used between a small number of trusted people.. “Molecular . sieves are crystalline metal . aluminosilicates. having a . three-dimensional . interconnecting network of silica and alumina . tetrahedra. . . Water is . removed from this network by heating to produce uniform cavities which selectively adsorb molecules of a specific size. www.drfrostmaths.com. Last modified: . 26. th. . November 2015. Objectives: . Have an appreciation of properties of integers (whole numbers), including finding the Lowest Common Multiple, Highest Common Factor, and using the prime factorisation of numbers for a variety of purposes. Oct. __. CONNECT - . Name_____ 6__ Lesson 4 – Prime and Composite Oct. __. CONNECT - . If you can only make 1 pair of factors with the number,. 1 and itself. , then the number is called a ____________. k. not a multiple of . p, . then gcd(. k,p. )=1.. If . i . . j (mod p). , then. i·k . . j. ·k. (mod p). Therefore,. . k mod p, 2k mod p, …, (p-1)k mod p. are all different numbers. . When Will I Ever Use Prime and Composite Numbers?. If you are baking cupcakes for a birthday party, you will be able to know if the amount you baked can be divided evenly between your friends. . Will you have leftovers? If it is a prime number, you know there will be leftovers!. Factoring: Given a number N , express it as a product of its prime factors. .. . Primality. : Given a number N, determine whether it is a prime. . Factoring is hard. Despite centuries of efforts the fastest methods for factoring a number N take time exponential in number of bits of N.. What is a composite number?. Give an example of each.. Greatest Common Factor. Mr. . Haupt. CC.2.1.8.E.1. Greatest Common Factor. The Greatest Common Factor, or GCF, is the largest number that goes in to every number given..