In the history of ancient Greece has been listed as a name identifier triple Pythagoras Pythagoras, but in the script Babylonian history Plimto rolls 322 in Babylonia also famed Triple babilonian. But popularity is not as popular as triple Babilonian introduced triple Pythagoras. However, both of these concerns at first glance seem similar, they are actually particularly a difference where the Babylonian Triples required elements forming the sides of the triangle must 2uv elbows, u-v ^ 2 ^ 2, u ^ 2 + v ^ 2. All of these numbers should be relatively prime and have no prime factors other than 2, 3, 5. As an example of the triple Babylonia, numbers 56, 90, 106 is the number of triple Babylonia. Because according to the terms (2uv, u-v ^ 2 ^ 2, u ^ 2 + v ^ 2) allows established values u and v respectively 9 and 5. While it's triple digits 28, 45, 53 is not included Babylonian triple. Because u = 7 and v is not an integer. Compared with triple Pythagoras, triple 28, 45, 53 numbered triple Pythagoras. In sederhannya Triple Babylonia certainly Pythagoras and triple triple Babylonian Phtagorasbelum course.
Prime Numbers Ancient Greek Period
Primes in Euclid's work contained in a book to -9 Elements stated that prima bilanagn will not end (There is no Last Prime). The statement has been proven using evidence contradiction Euclid. In the book Euclid also wrote the theory of Fundamental Arithmetic which reads "Every integer can be written as the product of prime numbers in a basic form that is unique". This is what we now know are looking for prime factors of a number.
The development of the next prime number in ancient Greece recognized the invention sieve of Eratosthenes. This filter is used to determine the number of primes. The stages or steps to determine prime numbers with the Sieve of Eratosthenes method as follows,
Arrange the natural numbers in a sequence of less than 50
- Remove number 1 because 1 is not a prime number
- Remove number multiples of 2, except 2
- Remove number multiples of 3, except 3
- Remove number multiples of 5 except 5
- Remove number multiples of 7, except 7
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| sieve of Eratosthenes |
The existence of a formula to predict the number of prime numbers less than n, followed by the discovery by Ernst Meissel. Meissel able to show the number of prime numbers less than 108 out of 5,761,455 in 1870. Bertelsen, continuing Ernst calculations performed in 1893. The results obtained Bertelsen announced that many prime numbers less than 109 in 50847478. However, this result was reformed on DH Lehmer 1959.
Prime Numbers Modern Mathematics
Lehmer menungkapkan Bertelsen mistake many bilanagn primed to aangka 50847534. In addition Lehmer further strengthen research that there are less than 1010 primes of numbers up 455052511. However mathematicians conduct research, until now there has been no practical a formula that can be used untukmenentukan a primes.
Some mathematician has stated formula for primes which is 2n-1 for n primes. Instead 2n-1 for n is not a prime number, not prime. However, these formulations prove wrong his evidence in 1640, Pierre de Fermat successfully demonstrated that it is wrong for n = 29 and some time later Euler showed that this time it is true for n = 31.
The development of modern primes have been using computing technologist. 1951 Meller and Wheeler began the era of electronic calculating machine -EDSA in Cambridge England and found some primes, namely: k.M127 + 1 to k = 114, 124, 388, 408, 498, 696, 738, 744, 780, 934 and 978, then obtained a record 79 new digit prime numbers. (M127) 2 + 1 (here M127 = 2127-1). In the following year Raphael Robinson with USING SWAC (Standards westeren Automatic Computer) discovered five new large prime numbers. At the time the program was first used on January 30, was found two primes (M521, M607), the next three prima found on June 25 (M1279), October 7 (M2203), and October 9 (M2281). Furthermore primes Riesel who find using the machine Sweden BESK M3217, M4253 and M4423 Hurwitz discovered by IBM 7090; Gilleis with ILLIAC-2 found the M9689, M9941 and M11213.
Tuckerman find M19937 with IBM360. Record primes the largest to date, held by Michael in the team of Michael Cameron, George Woltman, Scott Kurowski on November 14, 2001, managed to get prime numbers using a program written by George as a chain of GIMPS (Great Internet Mensenne Prime Search ) Internet database through Scott's PrimeNet. A prime number is a Mersenne Prime 39th that M13466917 consists of 4,053,946 decimal digits.
The most unique is the discovery Indlekofer and Ja'rai in November1995. They found the twin prime numbers are 242206083 x 23880 + 1 and 242206083 x 23880 - 1, both consisting of 11 713 decimal digits. The factorial primes, found by Caldwell in 1993 is 3610! -1, Which consists of 11 277 decimal digits.
