List of Prime Numbers
A prime number is a natural number with exactly two distinct divisors: itself and 1. And it is opposed to the compound numbers, which are those that have some natural divisor besides themselves and 1. The number one, by convention, is considered neither prime nor composite.
The prime numbers less than a hundred are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
The property of being a prime number is called primality. Sometimes we talk about an odd prime number to refer to any prime number greater than 2, since this is the only even prime number. Sometimes it denotes the set of all prime numbers by \ mathbb {P}.
The study of prime numbers is an important part of number theory, the branch of mathematics that includes the study of natural numbers. Prime numbers are present in some centuries-old conjecture such as the Riemann hypothesis and Goldbach's conjecture. The distribution of prime numbers is a recurring theme of research in number theory: if we consider individual numbers, the primes seem to be randomly distributed, but distribution "global" of primes follows well-defined laws.
Prime Numbers History
The notches present in the Ishango bone, dating from 20,000 years ago (prior to both the appearance of writing) and was found by archaeologist Jean de Heinzelin of Braucourt seems to isolate four prime numbers: 11, 13, 17 and 19. Some archaeologists interpret this as proof of knowledge of prime numbers. However, there are very few findings to discern the knowledge that was actually the man that period.
Many dry clay tabletsattributed to the civilizations that were happening in Mesopotamia during the second millennium BC show the arithmetic problem solving and witness the knowledge of the time. Calculations required knowing the inverse of the natives, which were also found in tablets. In the sexagesimal system the Babylonians used it to write the numbers, the reciprocals of the divisors of powers of 60 (numbers regular) are readily calculated by example, divide by 24 is equivalent to multiplying by 150 (2.60 +30) and run the sexagesimal point two places. The Babylonian mathematical knowledge needed a solid understanding of multiplication, division and factoring of the natives.
In Egyptian mathematics, the fraction calculation required knowledge of the transactions, the natural division and factoring.
The first indisputable proof of knowledge of prime numbers dates back to circa 300 BC. and is in Euclid's Elements (volumes VII to IX). Euclid defines primes, it probes that there are infinitely many of them, it defines the greatest common factor and least common multiple and provides a method for determining which today is known as the Euclidean algorithm. Elements also contain the fundamental theorem of arithmetic and how to build a perfect number from a Mersenne prime.
The sieve of Eratosthenes, attributed to Eratosthenes of Cyrene, is a simple method that lets you find primes. Today, however, the largest prime numbers found with the help of computers used by other faster and more complex algorithms.
After Greek mathematics, there were few advances in the study of prime numbers until the seventeenth century. In 1640 Pierre de Fermat stated (though without proof) Fermat's little theorem, later proved by Leibniz and Euler. You may be known well before a special case of this theorem in China.