Prime Numbers Hi friends, meeting you here after a long time, but assure you that will meet you here regularly (almost every month) with new interesting topics in mathematics. Last week only a famous American mathematician died in a road accident. His name was John Nash. He was a Noble laureate. He won noble prize in economics, in which he was never officially trained!!! John Nash We are going to discuss today prime numbers. I think numbers are very interesting to play with, you may like this topic. From upper primary years we start understanding types of numbers. But important aspect of classifying numbers we get by divisibility. We know based on this there are two types of numbers, Prime umbers and Composite numbers. Prime Numbers: A number which can be divided evenly only by 1 or itself and must be a whole number greater than 1. Composite Numbers: It is a number when it can be divided evenly by numbers other than 1 and itself.
Some of them are as follows Balanced Prime, Chen Prime, Circular Prime, Cousin Prime, Coprime, Cuban prime, Cullen Prime. Dihedral Prime, Eisenstein Prime, Factorial prime, Fibonacci Prime, Fortunate Prime, Gaussian prime, Good Prime, Happy Prime, Higgs Prime, Mersenne Prime, Minimal Prime, Palindromic Prime, Ramanujan Prime, Strong Prime , Super Prime, Twin Prime, Unique Prime, Wilson Prime, and so on. We know two types of primes, coprimes and twin primes. Coprimes: In number theory two integers a and b are said to be relatively prime, mutually prime or coprime if the only positive integer that evenly divides both of them is 1. That is only positive common factor of two numbers is 1. For example 14 and 15, but 14 and 21 are not. The number 1 and 1 coprime to every integer and they are only integers to be coprime with 0.
Cousin Primes: In mathematics Cousin Primes are prime numbers that differ by four. Compare these with twin primes, pairs of primes differ by two. The pairs of prime numbers that differ by six are called sexy primes. Cousin Primes (3,7);(7,11); 13,17); (19,23); (43,47); 67,71); (79,83); (97,101); …………….(907,911); (937,941); (967,971). These are up to 1000. Try and find other numbers in between. The only prime number belongs to two cousin prime pairs is ‘7’. As of May 2009 largest known Cousin prime was (p,p+4) form i) 474435381.2^{98394} 1 ii) 47445381. 2^{98394} 5 These numbers have 29629 digits and were found by Angle, Jobling and Augustine. Mersenne Primes: In mathematics Mersenne Prime is a number of the form M_{n}= 2^{n}1. If n is prime number then so is the 2^{n}1. Mersenne primes are sometimes have additional requirement that Additional requirement that n be prime, equivalent they be Pernicious Mersenne numbers. Smallest Composite Pernicious Mersenne number is 2^{11}1=2047=23x89 is a pseudo prime number. As of October 2014, 48 Mersenne Primes are known
Twin Primes : A twin prime is a prime numberthat has a prime gapof two, in other words, differs from another prime number by two, for example the twin prime pair (41, 43). Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes appear despite the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger due to the prime number theorem. The first few twin prime pairs are: (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), … A077800. An isolated prime is a prime number p such that neither p − 2 nor p + 2 is prime. In other words, p is not part of a twin prime pair. For example, 23 are an isolated primes since 21 and 25 are both composite. The first few isolated primes are 2, 23, 37, 47, 53, 67, 79, 83, 89, 97, … A007510
