primes

Eclipse 3.5 has a very nice feature to generate Java hashCode() functions. It would generate for example (slightly shortened:) class HashTest { int i; int j; public int hashCode() { final int prime = 31; int result = prime + i; result = prime * result + j; return result; } } (If you have more attributes in the class, result = prime * result + attribute.hashCode(); is repeated for each additional attribute. For ints .hashCode() can be omitted.) This seems fine but for the choice 31 for the prime. It is probably taken from the hashCode implementation of Java String , which was used for

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 formed? 4x^2+y^2, 3x^2+y^2 and 3x^2-y2 The algorithm in wikipedia talks about modulo sixty but I dont understand how/where that is used in the psudocode below. How are these reminders 1,5,7 and 11 found? Below is the pseudocode from Wikipedia for reference: // arbitrary search limit limit ← 1000000 // initialize the sieve for i in [5, limit]: is_prime(i

I have a set of prime numbers and I have to generate integers using only those prime factors in increasing order. For example, if the set is p = {2, 5} then my integers should be 1, 2, 4, 5, 8, 10, 16, 20, 25, … Is there any efficient algorithm to solve this problem? The basic idea is that 1 is a member of the set, and for each member of the set n so also 2 n and 5 n are members of the set. Thus, you begin by outputting 1, and push 2 and 5 onto a priority queue. Then, you repeatedly pop the front item of the priority queue, output it if it is different from the previous output, and push 2

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)}}} This is an implementation of the Sieve of Eratosthenes algorithm in R. sieve <- function(n) { n <- as.integer(n) if(n > 1e6) stop("n too large") primes <- rep(TRUE, n) primes[1] <- FALSE last.prime <- 2L for(i in last.prime:floor(sqrt(n))) { primes[seq.int(2L*last.prime, n, last.prime)] <- FALSE last.prime <- last.prime + min(which(primes[(last.prime+1):n])) } which

This c++ code prints out the following prime numbers: 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97. But I don't think that's the way my book wants it to be written. It mentions something about square root of a number. So I did try changing my 2nd loop to for (int j=2; j<sqrt(i); j++) but it did not give me the result I needed. How would I need to change this code to the way my book wants it to be? int main () { for (int i=2; i<100; i++) for (int j=2; j<i; j++) { if (i % j == 0) break; else if (i == j+1) cout << i << " "; } return 0; } A prime integer number is one that

I wrote a prime number generator using Sieve of Eratosthenes and Python 3.1. The code runs correctly and gracefully at 0.32 seconds on ideone.com to generate prime numbers up to 1,000,000. # from bitstring import BitString def prime_numbers(limit=1000000): '''Prime number generator. Yields the series 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 ... using Sieve of Eratosthenes. ''' yield 2 sub_limit = int(limit**0.5) flags = [False, False] + [True] * (limit - 2) # flags = BitString(limit) # Step through all the odd numbers for i in range(3, limit, 2): if flags[i] is False: # if flags[i] is True: continue

How to write a Program to find n primes after a given number? e.g. first 10 primes after 100, or first 25 primes after 1000. Edited: below is what I tried. I am getting output that way, but can we do it without using any primality-testing function? #include<stdio.h> #include<conio.h> int isprime(int); main() { int count=0,i; for(i=100;1<2;i++) { if(isprime(i)) { printf("%d\n",i); count++; if(count==5) break; } } getch(); } int isprime(int i) { int c=0,n; for(n=1;n<=i/2;n++) { if(i%n==0) c++; } if(c==1) return 1; else return 0; } Sure. Read about the Sieve of Eratosthenes . Instead of checking

I would just like to ask if this is a correct way of checking if number is prime or not? because I read that 0 and 1 are NOT a prime number. int num1; Console.WriteLine("Accept number:"); num1 = Convert.ToInt32(Console.ReadLine()); if (num1 == 0 || num1 == 1) { Console.WriteLine(num1 + " is not prime number"); Console.ReadLine(); } else { for (int a = 2; a <= num1 / 2; a++) { if (num1 % a == 0) { Console.WriteLine(num1 + " is not prime number"); return; } } Console.WriteLine(num1 + " is a prime number"); Console.ReadLine(); } Soner Gönül var number; Console.WriteLine("Accept number:"); number