Sieve of Eratosthenes : A basic implementation

The Sieve of Eratosthenes is a process to find all primes not exceeding a specific positive integer. The process is simple. First all the numbers within the range is populated in a list.The process strikes out all the numbers in the list which are multiple of some previous number. This strike-out process starts with the integer 2, thus first all the multiple of 2 upto the limit n are striked out. Note that the number 2 itself is not striked out, because it is not a multiple of any integer lesser than it (except 1). Next the just following unstriked integer is selected, which is in this case 3, and then all the multiples of 3 are striked out from the like, and again the next unstriked out integer is selected and the process continues until no such integer remains in the list which is unstriked and a multiple of some integer lesser that it. Note that the next integer to strike out after the ith unstriked integer is i * i , as all the multiples of i less than i are striked in the previous passes. At the end if the process only those numbers will be still unstriked in the list which are not a multiple of some other integer lesser that it, thus only the prime numbers will remain unstriked in the list. At the end of the process the list can be rescanned and the unstriked integers could be found.
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Generating Twin Primes, Cousin Primes and Sexy Primes

Twin Prime: A twin prime is a set of two prime numbers whose absolute difference is 2. Let p1 and p2 primes such that p2 – p1 = 2, then the set { p1 , p2 } are twin primes.

Objective Of The Article

The objective of this article is to describe the basic algorithm to search for the twin primes first, and then make some modifications to make it better and faster. At last we present the final code

Article Revision: 2

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