fastest way to generate prime numbers Most algorithms for finding prime numbers use a method called prime sieves Generating prime numbers is different from determining if a given number is a prime or not For that we can use a primality test such as
Prime sieves are almost always faster Prime sieving is the fastest known way to deterministically enumerate the primes There are some known formulas that can calculate the next prime but there is no known way to express the next prime in I assume you mean Given n what is the fastest known algorithm that generates all prime numbers p le n Currently it is the Sieve of Atkin And what is the fastest known algorithm that generates any infinite subset of the prime numbers
fastest way to generate prime numbers
fastest way to generate prime numbers
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In Java How To Find If Number Is Prime Or Not Best Way To Generate
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For bulk prime generation in the 64 bit range the segmented Sieve of Eratosthenes is the fastest method Implementation matters but the current fastest codes primesieve and yafu use this and it s faster than Sieve of Atkin e g primegen when similar optimizations are applied The fastest ways of generating primes is through any of the sieving algorithms where you cross out multiples of the already known primes starting with the prime 2 until you find a lowest number that is not a multiple of any of the already known primes and then you add that prime and cross out multiples of that prime and so on
Primesieve is a command line program and C C library for quickly generating prime numbers It is very cache efficient it detects your CPU s L1 L2 cache sizes and allocates its main data structures accordingly If you want to generate primes from 1 to whatever then the fastest way is probably a wheeled Sieve as implemented here which can typically test more than 3 000 000 candidate primes a second on an average laptop and that s using an unoptimized language like VB and factor the non primes to boot In c it could be
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NextPrime 2 return primes This has been optimised by only testing for divisibility up to the square root of the number being tested and by only testing odd numbers This can be further optimised by testing only numbers of the form 6k 1 5 or 30k 1 7 11 13 17 19 23 29 or so on Note The easiest and fastest way to determine modulo 90 congruence of a whole number is to reduce all digits antecedant to the number s terminating digit to their digital root For example the 1st three digits of 2497 reduce to digital root 6 leaving 67 which equates to 2497 67 mod 90
1 Efficient prime number generating leads to some algorithms being displayed as fast Up to PG7 8 which does takes 65786 seconds to generate the prime numbers 1 000 000 000 Primesieve however does this in 0 2 seconds The system specifications used for the tests are a bit off But I can imagine primesieve uses some highly advanced Apart from Sieve of Eratosthenes method to generate Prime numbers we can implement a new Algorithm for generating prime numbers from 1 to N It might be amazing to know that all the prime numbers 5 can be traced from a pattern Let s try to understand the series Series 1 5 6 11 11 6 17 17 6 23 23 6 29
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fastest way to generate prime numbers - A well known example is the RSA algorithm During the key generation step you have to choose 2 primes p and q and calculate their product n p q The security of RSA is based on the fact