PPT-Prime Algorithms

Presented by Alex Atkins Whats a Prime An integer p gt 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 gt 2 is either a prime or can be expressed as a product of a primes. Lessons Learned.. Benefits.. Overview MCTP project. Administrative support is crucial!. Secretarial support.. W9s, waivers, created . reqs. , reserving rooms, reviewing applications, details all over the place!. Prime numbers and factors.. Prime numbers. Prime numbers divide by themselves and one.. So… 3=3*1…or… 13=13*1. But 16 divides 16*1 and 8*2 and 4*4. So you see that prime numbers are very specific.. Jordi Cortadella. Department of Computer Science. Prime number. A . prime number. . is a natural number that has exactly two . distinct. divisors: 1 and itself.. . 1 is not prime. . . Mathematics. . Number Theory. By Megan Duke – Muskingum University. Review . Prime – a natural number great than 1 that has no positive divisors other than 1 and itself.. Quadruplet – a grouping of 4. Lessons Learned.. Benefits.. Overview MCTP project. Administrative support is crucial!. Secretarial support.. W9s, waivers, created . reqs. , reserving rooms, reviewing applications, details all over the place!. 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.. Problem - a well defined task.. Sort a list of numbers.. Find a particular item in a list.. Find a winning chess move.. Algorithms. A series of precise steps, known to stop eventually, that solve a problem.. 1.2 & 2.0 . Agenda. 1. 2. 3. 4. Cisco Prime Infrastructure Vision, Strategy and Roadmap. Cisco Prime Infrastructure Migration and . Licensing. Cisco Prime . Infrastructure 2.0 . Feature Highlights. 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. . Seth Futrell, Matthew Ritchie, . Dakota Perryman, Mark Thompson . (Tag’s 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 .. 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. . 10 Bat Algorithms Xin-She Yang, Nature-Inspired Optimization Algorithms, Elsevier, 2014 The bat algorithm (BA) is a bio-inspired algorithm developed by Xin-She Yang in 2010. 10.1 Echolocation of Bats Cyclic group G of order q with generator g.  G.  . G = {g. 0. , g. 1. , …, g. q-1. }. For any h .  G, define . log. g. h .  {0, …, q-1} as. . log. g. h = x  . 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..