MHB Integer Factorization: Help with Pollards P-1 & Quadratic Sieve

AI Thread Summary
The integer 2896753 can be factored using Pollard's p-1 method, but a large factor base, specifically primes up to 31, is necessary for effective results. The quadratic sieve is generally reliable for numbers of this size, indicating potential issues with the current implementation being used. It is recommended to perform trial division up to the first ten thousand primes before attempting more complex methods like ECM. The discussion emphasizes the importance of the right approach and tools for successful integer factorization. Proper implementation and method selection are crucial for effective factorization of integers.
behnazbarzi
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hey guys, I wonder if you could help me... i cannot factor the integer 2896753 by pollards p-1 method and the quadratic sieve .
 
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What factor base are you using for Pollard's p - 1? It will work, though you need a fairly large factor base for such a small input number (primes up to 31) unless you are using the two-step variant.

As for the quadratic sieve, it pretty much always works for sufficiently large numbers (including yours) so obviously the implementation you are using is broken. How are you carrying out the quadratic sieve?

To be fair though for a number of this size I'd start by carrying out trial division up to the first ten thousand primes (which would factor it) and then directly moving on to ECM.
 

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