PPT-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. 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 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. . . Number Theory. Dr J Frost (jfrost@tiffin.kingston.sch.uk). 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. 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. 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. Lesson . 3.01. After completing this lesson, you will be able to say. :. I . can. find the least common multiple of two whole numbers. .. I . can. find the greatest common factor of two whole numbers. &. Prime Factors. Jedward are selling some stationary at their . concert. . They want to sell a pack containing the same number of erasers and pencils, but they are coming from two different suppliers. Pencils come in packages of 18, erasers come in packages of 30. Jedward want to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil to see if their fans will buy them. How many packages of pencils and erasers will Jedward. 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. . by Carol Edelstein. Definition. Product. – An answer to a multiplication problem.. . 7 x 8 = 56. Product. Definition. Factor. – a number that is multiplied by another to give a product.. . 7 x 8 = 56. 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 .. 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? Maria Murphy. Central Florida Math Circle. University of Central Florida . Department of Mathematics . What is a Palindrome? . A palindrome is a word or phrase that reads the same forwards and backwards. . 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..