factorization

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 : filter ((==1) . length . primeFactors) [3,5..] primeFactors n = factor n primes where factor n (p:ps) | p*p > n = [n] | n `mod` p == 0 = p : factor (n `div` p) (p:ps) | otherwise = factor n ps problem_3 = last (primeFactors 317584931803) My naive reading of this is that primes is defined in terms of primeFactors , which is defined in terms of primes

When following the procedure on wikipedia for wheel factorization , I seem to have stumbled into a problem where the prime number 331 is treated as a composite number if I try to build a 2-3-5-7 wheel. With 2-3-5-7 wheel, 2*3*5*7=210. So I setup a circle with 210 slots and go through steps 1-7 without any issues. Then I get to step 8 and strike off the spokes of all multiples of prime numbers, I eventually strike off the spoke rooted at 121, which is a multiple of 11, which is a prime. For the spoke rooted at 121, 121 + 210 = 331. Unfortunately, 331 is a prime number. Is the procedure on

Alright, so I have a huge number f . This number is just over 100 digits long, actually. I know that the factors are of approximately the same size. If I have limited resources and time, what language and algorithm should I use? I am including the length of time to code the algorithm in the restricted time. Thoughts? EDIT: By limited, I mean in the least amount of time possible. Mysticial The state-of-the-art prime factorization algorithm is the quadratic sieve and its variants. For numbers larger than 100 digits, the number sieve becomes more efficient. There's an open-source implementation

Could anyone point me to a library/code allowing me to perform low-rank updates on a Cholesky decomposition in python (numpy)? Matlab offers this functionality as a function called 'cholupdate'. LINPACK also has this functionality, but it has (to my knowledge) not yet been ported to LAPACK and hence isn't available in e.g. scipy. I found out that scikits.sparse offers a similar function based on CHOLMOD, but my matrices are dense. Is there any code available for python with 'cholupdate''s functionality that's compatible with numpy? Thanks! Here is a Python package that does rank 1 updates and

#include <iostream> using namespace std; void whosprime(long long x) { bool imPrime = true; for(int i = 1; i <= x; i++) { for(int z = 2; z <= x; z++) { if((i != z) && (i%z == 0)) { imPrime = false; break; } } if(imPrime && x%i == 0) cout << i << endl; imPrime = true; } } int main() { long long r = 600851475143LL; whosprime(r); } I'm trying to find the prime factors of the number 600851475143 specified by Problem 3 on Project Euler (it asks for the highest prime factor, but I want to find all of them). However, when I try to run this program I don't get any results. Does it have to do with how

I need to get all the prime factors of large numbers that can easily get to 1k bits. The numbers are practically random so it shouldn't be hard. How do I do it efficiently? I use C++ with GMP library. EDIT: I guess you all misunderstood me. What I mean by prime a number is to get all prime factors of the number. Sorry for my english, in my language prime and factor are the same :) clarification (from OP's other post): What I need is a way to efficiently factor(find prime factors of a number) large numbers(may get to 2048 bits) using C++ and GMP(Gnu Multiple Precession lib) or less preferably

I'm working on a Project Euler problem which requires factorization of an integer. I can come up with a list of all of the primes that are the factor of a given number. The Fundamental Theorem of Arithmetic implies that I can use this list to derive every factor of the number. My current plan is to take each number in the list of base primes and raise its power until it is no longer an integer factor to find the maximum exponents for each prime. Then, I will multiply every possible combination of prime-exponent pairs. So for example, for 180: Given: prime factors of 180: [2, 3, 5] Find maximum