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Questions tagged [primes]

Primes or prime numbers are integers greater than 1 which are divisible only by themselves and 1, i.e.: 2, 3, 5, 7, 11, ... .

See Wikipedia on primes.

If your program for checking or computing prime numbers doesn't work, please check the following points before posting a question:

  • If it is too slow, try testing divisibility only up to and including the square root. If you want to compute all primes in a range better use the sieve of Eratosthenes, implemented properly it will be much faster.

  • If your algorithm says square numbers are prime you neglected the and including part above.

  • Check for overflow. n * n overflows a 32 bit signed integer for n > 46340. The sum of the first two million primes for Project Euler problem 10 will also overflow a 32 bit integer.

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Finding prime numbers with the Sieve of Eratosthenes (Originally: Is there a better way to prepare this array?)

Note: Version 2, below, uses the Sieve of Eratosthenes. There are several answers that helped with what I originally asked. I have chosen the Sieve of Eratosthenes method, implemented it, and changed the question title and tags appropriately. …
eleven81
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Sieve of Atkin explanation

I am doing a project at the moment and I need an efficient method for calculating prime numbers. I have used the sieve of Eratosthenes but, I have been searching around and have found that the sieve of Atkin is a more efficient method. I have found…
marc lincoln
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What is the fastest deterministic primality test for numbers in the range 2^1024 to 2^4096?

I am writing an implementation of a cryptography protocol. So far I've been having a difficult time finding the fastest deterministic primality test for 1024-bit to 4096-bit integers (308- to 1233-digit numbers). I am aware of several options but…
jnm2
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How do I generate Primes Using 6*k +- 1 rule

We know that all primes above 3 can be generated using: 6 * k + 1 6 * k - 1 However we all numbers generated from the above formulas are not prime. For Example: 6 * 6 - 1 = 35 which is clearly divisible by 5. To Eliminate such conditions, I…
Uma Kanth
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Using LINQ to generate prime numbers

Following is an interview question: The following one-liner generates and displays the list of first 500 prime numbers. How would you optimize it using parallel LINQ while still keeping it a SINGLE C# STATEMENT: MessageBox.Show(string.Join(",", …
dotNET
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The Sieve of Atkin

I have been trying to learn algorithms for generating prime numbers and I came across Sieve of Atkin on Wikipedia. I understand almost all parts of the algorithm, except a few. Here are the questions: How are the three quadratic equations below…
Shiv
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Explain this chunk of haskell code that outputs a stream of primes

I have trouble understanding this chunk of code: let sieve (p:xs) = p : sieve (filter (\ x -> x `mod` p /= 0) xs) in sieve [2 .. ] Can someone break it down for me? I understand there is recursion in it, but thats the problem I can't understand…
nubela
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Write the biggest prime

I'm trying to solve the biggest prime programming praxis problem in C#. The problem is simple, print out or write to file the number: 257,885,161 − 1 (which has 17,425,170 digits) I have managed to solve it using the amazing GNU Multiple Precision…
marcob
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How many iterations of Rabin-Miller should I use for cryptographic safe primes?

I am generating a 2048-bit safe prime for a Diffie-Hellman-type key, p such that p and (p-1)/2 are both prime. How few iterations of Rabin-Miller can I use on both p and (p-1)/2 and still be confident of a cryptographically strong key? In the…
jnm2
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Generate a list of primes up to a certain number

I'm trying to generate a list of primes below 1 billion. I'm trying this, but this kind of structure is pretty shitty. Any suggestions? a <- 1:1000000000 d <- 0 b <- for (i in a) {for (j in 1:i) {if (i %% j !=0) {d <- c(d,i)}}}
Thomas
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Enumerate factors of a number directly in ascending order without sorting?

Is there an efficient algorithm to enumerate the factors of a number n, in ascending order, without sorting? By “efficient” I mean: The algorithm avoids a brute-force search for divisors by starting with the prime-power factorization of n. The…
Todd Lehman
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Determining if a given number is a prime in haskell

So I have devised the following function for seeing if a given number is a prime in Haskell (it assumes the first prime is 2): isPrime k = length [ x | x <- [2..k], k `mod` x == 0] == 1 it has the obvious pitfall of continuing the evaluation even…
devoured elysium
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How to optimize this Haskell code summing up the primes in sublinear time?

Problem 10 from Project Euler is to find the sum of all the primes below given n. I solved it simply by summing up the primes generated by the sieve of Eratosthenes. Then I came across much more efficient solution by Lucy_Hedgehog (sub-linear!). For…
Adam Stelmaszczyk
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How can I find the prime factors of an integer in JavaScript?

I was trying to find the prime factors of a number, recorded below as 'integer' using a for loop in javascript. I can't seem to get it working and I'm not sure whether it's my JavaScript or my calculation logic. //integer is the value for which we…
John the User
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Why is this Haskell code snippet not infinitely recursive?

To help me learn Haskell, I am working through the problems on Project Euler. After solving each problem, I check my solution against the Haskell wiki in an attempt to learn better coding practices. Here is the solution to problem 3: primes = 2 :…
Matthew
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