Prime number theorem

Abstract The Physics of Prime Numbers [1] Yeow Liiyung University of Leeds Introduces the prime numbers and the Riemann Hypothesis as an im- portant unsolved problem in mathematics, and suggests that there may be a physical interpretation or embodiment of the problem. Although several physical interpretations are on offer, this paper focuses primarily on how the primes may be connected to quantum physics and classical chaos, and seeks to compile evidence hitherto that this might be true. We take

The perfect number is a positive integer that is equal to the sum of its proper divisors. Earlier definitions of a perfect number were 'aliquot parts' of a number. An aliquot part means a proper quotient of a number. According to Webster’s dictionary, the term perfect number was first used in the 14th century. The discovery of such numbers was lost in prehistory. The smallest perfect number is six. It is the sum of its divisors one, two, and three. Other perfect numbers are twenty-eight, 128, and

Sophie Germain was born April 1st, 1776 in Paris, France. Sophie’s family was rich and counted as upper Classmen. Sophie was the middle child out of 2 others, Marie-Madeline Germain and Angelique-Ambroise Germain. She was brought into the world around times when it was frowned upon for women to be educated, not to mention that it was also a revolution year too. Sophie spent most of her time in the house reading in her Father’s collection of books. “Their eldest and youngest daughters, Marie-Madeleine

is the perfect number?” What they do not know is that there is more than just one perfect number; there are many. Today’s research tells us that there are forty-eight perfect numbers. A perfect number is a number that is equal to the sum of its positive divisors, excluding its self. 6=1+2+3 28=1+2+4+7+14 18=1+2+3+6+9 (= 21) To answer the question of what a perfect number is you need to know how to solve for a perfect number, who has been involved in coming up with perfect numbers, the criteria

In the play Proof, David Auburn, suggests that Catherine the main protagonist is into mathematics. Catherine’s father Robert was a mathematical genius as he was a professor at the University of Chicago. Catherine took care of him for five years while he was sick, which caused her to stop going to College. Robert died due to a mental illness. Catherine wrote a proof that not even Hal a Ph.D. graduate could have discovered. As she inherited her father’s mathematical genius, she is afraid that she might

Odd numbers were thought of as female and even numbers as male.” Out of all the numbers Pythagoras believed that the number ten was the holiest number. He believed this because it was made up of the first 4 digits, and when arranged in 4 rows of points it made a triangle. Pythagoras also discovered prime numbers and composite numbers. He also did some research relating to perfect numbers (the sum of the divisors is equal to the number). The number 6 is an example of a perfect number. (3+2+1=6)

chemistry. The attempts created to solve Fermat 's Last Theorem also advanced the path for generalizing integer arithmetic, and developed the concept of a ring. In Fermat’s Last Theorem, it is stated: The equation xn+ yn= zn has no solution for positive integers, x, y, z when n > 2. Fermat wrote “I have discovered a truly remarkable proof which this margin is too small to contain.” (Diophantus 's Arithmetica) One attempt to prove Fermat’s Last Theorem had been in the year 1753, when Euler had brought

be prime, and suppose it is equal to x2 -y2 that is, to (x+y)(x-y). Now, by hypothesis, the only basic, integral factors of n and n and unity, hence x+y=n and x-y=1. Solving these equations we get x=1 /2 (n+1) and y=1 /2(n-1). -He gave a proof of the statement made by Diophantus that the sum of the squares of two numbers cannot be the form of 4n-1. He added a corollary which I take to mean that it is impossible that the product of a square and a prime form 4n-1[even if multiplied by a number that

Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series. Ramanujan was born in his grandmother's house in Erode on December 22, 1887. When Ramanujan was a year old his mother took him to the town of Kumbakonam, near Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. When he was five years old, Ramanujan went to the primary

circle is bisected by its diameter, that the base angles of an isosceles triangle are equal and that vertical angles are equal. * Accredited with foundation of the Ionian school of Mathematics that was a centre of learning and research. * Thales theorems used in Geometry: 1. The pairs of opposite angles formed by two intersecting lines are equal. 2. The base angles of an isosceles triangle are equal. 3. The sum of the angles in a triangle is 180°. 4. An angle