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GIMPS has discovered a new largest known prime number : 2 -1 24,, digits.

Chris K. GIMPS has discovered a new largest known prime number : 2 -1 24,, digits The most efficient way to find all of the small primes say all those less than 10,, is by using a sieve such as the Sieve of Eratosthenes ca BC : Make a list of all the integers less than or equal to n and greater than one.

Strike out the multiples of all primes less than or equal to the square root of n , then the numbers that are left are the primes.

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For example, to find all the primes less than or equal to 30, first list the numbers from 2 to Keep it and cross out all of its multiples. We know that all multiples less than 9 i. Notice we just found these primes without dividing.

In fact the problem with the algorithm as presented above is not really speed it uses O n log n log log n bit operations , but rather space it is O n. So for large n we usually use a segmented sieve.

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  • Bayes and R. Hudson , "The segmented sieve of Eratosthenes and primes in arithmetic progression," Nordisk Tidskr.

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    Informationsbehandling BIT , 17 :2 MR Bressoud89 D. Bressoud , Factorizations and primality testing , Springer-Verlag, MR 91e [pseudocode implementation on page 19] [QA F3B73] Pritchard87 P.

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    Pritchard , "Linear prime-number sieves: a family tree," Sci. Programming , 9 :1 MR 88j [Comparison of various sieves] [A comparison of recent sieves such as the sieve of Eratosthenes. ISBN Code is provided in Pascal.

    Previous edition was vol.