(DOWNLOAD) "Certain Forms of Even Numbers and Their Properties" by Global Journal of Pure and Applied Mathematics ~ eBook PDF Kindle ePub Free
eBook details
- Title: Certain Forms of Even Numbers and Their Properties
- Author : Global Journal of Pure and Applied Mathematics
- Release Date : January 01, 2009
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 66 KB
Description
Introduction Some problems of combinatorics have been found in number theory. The number theory has been occupying a field of conjectural problems. Among these conjectural problems (statements), the conjectural problems of prime number has been playing an important role. The scientists in general and number theorist in particular have been thinking since the establishment of the conjectures to get the formal proof of them. Some sophisticated conjectural problems, quite a few of them are twin prime conjecture, mersenne prime conjecture and Goldbach conjecture. The twin prime conjecture states that if p is prime, then there exist infinitely prime pair (p, p+2). Similarly, the mersenne prime conjecture states that if p is prime, then [2.sup.p]-1 is also a prime. The Goldbach conjecture [1742] is that every even number larger than 2 can be expressed as a sum of two primes. Besides, the existence of prime between [n.sup.2] and [(n+1).sup.2] is also a conjectural statements. Again it is found that there are many primes of the form 4n+3, 6n+5 and 8n+5 for n [greater than or equal to] 1. Number theorist have been searching various properties of primes which can be actually supposed as a never ending theory. One of the very important non settled problems is to find out a general formula or functional relationship in terms of n where n [greater than or equal to] 1. It has been found that [n.sup.2]-n +41 is prime for 1 [less than or equal to] n [less than or equal to] 40 [5]. But the prime numbers obtained from this formula are not consecutive. Another formula [n.sup.2]-79n +1601 has also been forwarded for 1 [less than or equal to] n [less than or equal to] 79, from which only 79 primes have been calculated [1].
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