 mersenneforum.org Are these polynomials being generated correctly?
 Register FAQ Search Today's Posts Mark Forums Read 2016-12-02, 19:01 #1 Sam Kennedy   Oct 2012 2·41 Posts Are these polynomials being generated correctly? I'm just double checking that the polynomials in my upcoming implementation of the MPQS are being generated correctly: n = 1287871475892167 First prime is near sqrt(sqrt(2*N)/M), where M is the sieve size, in this case: 500,000 Polynomials generated (Ax + B)^2 - N: A: 121 B: 109 A: 169 B: 51 A: 361 B: 345 A: 1849 B: 533 A: 2209 B: 1655 A: 2809 B: 2757 This is how I'm generating them: After finding a prime Q close to sqrt(sqrt(2*N)/M), which is a quadratic residue mod N, I set: A = Q^2 h = N^((Q+1)/4) mod Q v = (2h)^-1 * ((N - h^2)/Q) mod Q B = h + vQ mod Q^2 If B is even, then B = A - B. In the trial division stage, values of X are plugged into the polynomial (Ax + B)^2 - N, and divided by A, before being divided over the factor base. Is this process correct? Are the polynomials above correct for the given input? Thank You Last fiddled with by Sam Kennedy on 2016-12-02 at 19:02  Thread Tools Show Printable Version Email this Page Similar Threads Thread Thread Starter Forum Replies Last Post EdH Msieve 4 2017-02-03 15:13 chalsall Software 16 2014-01-03 15:55 Puzzle-Peter Conjectures 'R Us 0 2013-08-15 13:45 ixfd64 Lounge 1 2012-06-23 12:43 Unregistered Software 15 2003-12-14 20:27

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