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. . & Prime Factorization. All About Primes. 1. Click to Advance. Suggestion:. Work with scratch paper and pencil as you go through this presentation.. The . Factors. of a Whole Number are:. All . the . Prime and Composite Numbers. Prime Number. A prime number is any whole number that has only two factors, itself and 1. . Example:. 5. It only has two factors, 5 and 1. 5 x 1= 5. What are other examples of prime numbers?. 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.. 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.. There is a rule for finding any prime (. eg. the . ). . There . is a way to find out how many primes are below any number (. eg. Number of primes below 1000). . There . is no end to the prime numbers. . What’s a Prime Number?. Lots of definitions out there. My Favorite (recursive): . “an integer greater than 1, that is not divisible by any smaller primes”. Note: The above is equivalent to (but feels less restrictive than) the more standard: . “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. Today’s Agenda. 2. What Is TRICARE?. 3. Other Important Information:. . The Affordable Care Act. 4. What Is TRICARE? TRICARE Stateside Regions. 5. What Is TRICARE?: TRICARE Overseas Program. 6. TRICARE Eligibility:. Everyday Math Lesson 1.9. Lesson Objectives. I can tell the difference between powers of ten written as ten raised to an exponent. .. I can show powers of 10 using whole number exponents. . Mental Math. 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!. This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola.
Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola.
The ellipse equation can be written in the following form: |p(k)| + |p(t)| = 2n.
The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n.
Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...),
k and t are indices of prime numbers,
2n is a given even number,
k, t, n ∈ N.
If we construct ellipses and hyperbolas based on the above, we get the following:
1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points.
2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.
Will there be any new thoughts, ideas about this?