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On the Prime Number Subset of the Fibonacci Numbers Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach On the Prime Number Subset of the Fibonacci Numbers Lacey Fish1 Brandon Reid2 Argen West3 1Department of Mathematics Louisiana State University Baton Rouge, LA 2Department of Mathematics University of Alabama Tuscaloosa, AL 3Department of Mathematics University of Louisiana Lafayette Lafayette, LA Lacey Fish, Brandon Reid, Argen West SMILE Presentations, 2010 LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions What is a sieve? What is a sieve? A sieve is a method to count or estimate the size of “sifted sets” of integers. Well, what is a sifted set? A sifted set is made of the remaining numbers after filtering. Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions What is a sieve? What is a sieve? A sieve is a method to count or estimate the size of “sifted sets” of integers. Well, what is a sifted set? A sifted set is made of the remaining numbers after filtering. Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions History Two Famous and Useful Sieves Sieve of Eratosthenes Brun’s Sieve Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions History Two Famous and Useful Sieves Sieve of Eratosthenes Brun’s Sieve Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions History The Sieve of Eratosthenes Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Lacey Fish, Brandon Reid, Argen West LSU, UA, ULL Sieve Theory Introduction to Sieves Fibonacci Numbers Fibonacci sequence mod a prime Probability of Fibonacci Primes Matrix Approach Basic Definitions Brun Sieve The Brun sieve is a generalized method compared to the Eratosthenes sieve. It allows us to sieve any set A with a designated set P: It is formally stated as: [
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