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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

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Better EssaysHow 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

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Good Essayssolace 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

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Satisfactory EssaysRecurring Decimals Infinite yet rational, recurring decimals are a different breed of numbers. Mathematicians, in turn, have been fascinated by these special numbers for over two thousand years. The Hindu-Arabic base 10 system we use today was inspired by the Chinese method of decimals which was actually around 10000 years old. Decimals may have been around for a very long time, but what about recurring decimals? In fact the ancient Greeks were one of the first to deal with recurring decimals

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Powerful Essaysinfinitely many prime1 numbers Proof. Suppose there are only finitely many primes p1, p2, . . . , pn. Consider the integer P = p1p2 ···pn+1. Let p be prime dividing P. If p is equal to pi for some i, then p divides both P and p1p2 · · · pn. This implies that p also divides their difference P − p1p2 · · · pn = 1A prime number p is an integer greater than one which is only divisible by one and itself ￼ ￼1, which is absurd. This contradicts our assumption that there are no other primes then p1,p2,...,pn

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Good Essaysmake sure that there would be no interpretation errors, and he also was the first known person to prove that there is no such thing as the ‘largest prime number’ because if you one to the product of all of the previous prime numbers you’ll get a large prime number. Thus, the process goes on forever and ever so there can be no one, true ‘largest prime number (“Euclid, the Father of

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Better Essaysdecryption) exponent d, which must be kept secret. p, q, and f(n) must also be kept secret because they can be used to calculate d. " The RSA algorithm is used in almost all secure transmissions over the Internet. The basic idea is that the prime numbers are so big and the time to decode so large that the message remains secure. The mathematic is so complicated to discuss easily here, so a discussion of how to use the RSA in practice is discussed.

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Satisfactory Essaysall fields in some form or another, and it is the only truly universal language. Even fields considered the opposite of mathematics, such as literature, are filled with different forms of math. Music is based very heavily on numbers, and even religions hold different numbers as sacred. Of course one could say that all these examples are merely basic arithmetic. What about higher mathematics? Can we really use algebra, probability, calculus or any other higher form of math in today's society? The

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Powerful EssaysTheon of Smyrna tells us that Eratosthenes' work studied the basic definitions of geometry and arithmetic, as well as covering such topics as music. Eratosthenes also worked on prime numbers. He is remembered for his prime number sieve, the 'Sieve of Eratosthenes' which, in modified form, is still an important tool in number theory research. Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. Details were given in his treatise On the measurement of the Earth which

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Satisfactory EssaysUnraveling the complex and diverse nature of numbers has always been a fascinating ordeal for me; that is what makes and keeps me interested in the world of mathematics. Finding out new number patterns and the relationship between numbers is nothing short of a new discovery; that is how my interest into learning more about and exploring Fermat's Little Theorem came about. INTRODUCTION OF FERMAT'S LITTLE THEOREM Pierre de Fermat was a French mathematician whose contribution to analytic geometry

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