therefore cannot be dated earlier than 1660. Mr. Pierre de Fermat discovered many things in his lifetime. Some things that he did include: -If p is a prime and a is a prime to p then ap-1-1 is divisible by p, that is, ap-1-1=0 (mod p). The proof of this, first given by Euler, was known quite well. A more general theorem is that a0-(n)-1=0 (mod n), where a is prime...
solace in prime numbers about which the famous number theorist Carl Pomerance once remarked, “God may not play dice with the universe, but something strange is going on with the prime numbers.” Prime numbers have been of interest to mathematicians for centuries, and we owe much of our existing knowledge on the subject to thinkers who lived well before the Common Era––such as Euclid who demonstrated that there are infinitely many prime numbers around 300 BCE. Yet, for as long as primes have been an
Prime Numbers Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has
series of powers of two, then a prime number (Osborn). Take twenty-eight for example, its divisors are one, two, four, seven, and fourteen. One is two to the zeroth, two is two to the first, four is two squared and then there is seven the prime number. Euclid showed that if 2p−1 is prime then (2p−1)2p−1 is perfect. To find a perfect number from a prime number you would take the prime number and multiply it by the first number before it. For example take the prime number thirty-one. Its factors are
How can we find a large prime number People use numbers whenever they do math. Yet, do they know that each number in the number system has its own unique trait? Numbers such as 4 and 9 are considered square numbers because 2 times 2 is 4, and 3 times 3 is 9. There also prime numbers. Prime numbers are numbers that have exactly two divisors. The number one is not included because it only has one divisor, itself. The smallest prime number is two, then three, then five, and so on. This list goes
Analysis of The Prime of Miss Jean Brodice by Muriel Spark “The Prime of Miss Jean Brodie is a novel about a teacher’s dedication to her pupils. It is also about loyalty and betrayal.” The Prime of Miss Jean Brodie is a novel about a teacher’s dedication to her pupils. It is also about loyalty and betrayal. The novel emphasises the effects of dedication, loyalty and betrayal within a small group of people and the way in which they are all intertwined. It forces the reader to look at particular
The Dangers of Social Conformity Exposed in The Prime of Miss Jean Brodie Muriel Spark's The Prime of Miss Jean Brodie depicts the coming of age of six adolescent girls in Edinburgh, Scotland during the 1930's. The story brings us into the classroom of Miss Jean Brodie, a fascist school teacher at the Marcia Blaine School for Girls, and gives close encounter with the social and political climate in Europe during the era surrounding the second World War. Spark's novel is a narrative relating
The Importance of Taking Care of Hands and Feet Nail care was different during the ancient times through 1900s. Most women and men do not go into the nail shop for the importance of taking of their hands and feet. If they are really concerned, they should talk to someone about it instead of putting it aside. If they do not get help right away, it can cause many problems such as infections, diseases, and even both. It all started during the ancient roman times. At the time, nail care was part
Feet are a very important component of the human body because of the virtual function they play of ensuring mobility. Care and protection is important in ensuring healthy feet. Consider the following points in giving care to your feet. Wear appropriate shoes. Wearing the wrong type of shoes can cause deformities such as bunions, ingrown toe nails, cross over toes, hammer toes, corns and cracked heels. Avoid these by; Not wearing high heeled shoes for a long period of time as this leads to back
same story to the next person who of course was waiting outside of the classroom, until it got to the fourth person. The story that the fourth person ended up with was extremely dissimilar from what was initially told to the first person. This is a prime example of how rumors change while they are being said from one person to the other. There were two rumors in the experiment conducted for the rumor assignment. Both rumors were very different in context but both proved the same thing in the end. Rumor
step above the normal, ordinary curs. They have the ability to overstep normal bounds and transgress the rights of those who are simply ordinary. They are the prime movers--they have a right to transcend normal societal strictures to accomplish those things they have determined are valid in their conscience. Extraordinary men are the prime movers. He cites such extraordinary men as Newton, Mahomet, and Napoleon. He tells us that Newton had the right to kill hundreds of men if need be in order to
Prime of Miss Jean Broadie To be in Miss Broadie’s set was to be set apart from the rest of the school. They were outwardly looked upon with disdain. Inwardly, however, others were jealous of them for the distinction they received. Each girl in the Broadie set was held on a pedestal. Each had something special about them, reasons why they were chosen by Miss Broadie, and that puts them at higher regard. Each girl was famous in school for something. They really have very little in common
encryption is the foundation of public key cryptography security products. For example, credit card companies use the RSA algorithm for customers’ individual online WebPages. The credit card companies publish a big number on WebPages, which is made by big prime numbers using the RSA algorithm. Since neither computers nor people can factor such big numbers, the RSA encryption system has secured many customers’ information. The RSA encryption is related to the cipher of Julius Caesar (1300s) that shifts three
News Is it prime time or all the time? Media influence has become a social mainstay in contemporary society. Not only do newspapers, radio, television and magazines strive to inform and entertain, but they also hold a significant power over what people believe. Since its inception, the standard of media presence was long a tool of integrity and fairness. Newspersons and entertainers may have embellished here and there in order to put more flavor into a certain piece or program, but for the most
Prime Time for Education It would be a wonderful world if we could give our children a better future. Why not start by filling their little minds with a handful of education at an early age? In Arizona it has been a controversial subject on whether to fund full day kindergarten. In my research on the subject and the experience I have had with my own children full day kindergarten is all around a wonderful idea. There are benefits for children, parents and teachers. Benjamin Franklin once said, “An
Kim Campbell, Canada's first female Prime Minister, rose quickly in her political standings reaching, what she would find to be the height of her career only seven years after entering politics. It appeared like the loss of the 1993 election and the all around destruction of the Progressive Conservative party was completely Kim Campbell’s fault however actually was a joint effort by Brian Mulroney and Kim Campbell. Kim Campbell rose so quickly in her political status that she did not have the experience
Investigating the Phi Function The phi function is defined for any positive integer[IMAGE](n), as the number of positive integers not greater than and co-prime (have no factor other than 1 in common) to n Example So [IMAGE](12) = 4 because the integers less than 12 which have no factors in common with it except for 1 are 1,5,7,11 i.e. there is 4 of them. I started to investigate the phi function of numbers from 2 to 24 so I could find patterns, which I can use to create a formula
greatest Prime Minister of Canada was? Mackenzie King our 10thPrime Minister of Canada and by far one of our greatest. William Lyon Mackenzie King accomplished a lot in his twenty-0ne years of ministering our Country Canada! "It is what we prevent, rather than what we do that counts most in Government." (Mackenzie King august 26, 1936) This statement sums up the best secrets of Mackenzie King's success as prime minister, and perhaps, the key to governing Canada effectively. King's record of prime minister
Investigation of the Cooling of a Liquid in Cups with Different Materials Aim: To investigate how a liquid cools down in cups with different materials. Prediction: The factors which will affect the amount of heat loss are: § Material of the cup – Conduction § Colour – Radiation § Surface area of cup § Amount of water (surface area:volume ratio) § If the cup has a lid or not – Convection and Evaporation § Room temperature § Thickness of the cup § Temperature of the liquid
Heat Loss Investigation Aim To investigate how variations in surface area and volume ratios in organisms lead to variations in heat loss and retention. Introduction Large animals have the ability to retain heat more easily than smaller animals because they have a larger surface area to volume ratio. This is the what I am trying to prove in the experiment. There are examples of this in nature. In winter the robin fluffs its wings up in order to retain more heat. When it does this