factorint and factor is not the same thing. factorint allows you to specify various parameters for the factorisation. For example you can select which of the various factorisation algorithms are used by Pari to split your integer. You can also pass an integer to the factor functions telling you up to what size you want to check for factors.
This is very likely what the primality proof test does. In particular most efficient primality tests first try to find small factors by trial factoring. If it finds any it can immediately declare the number composite without doing an expensive primality proof. It is irrelevant at this point whether the primes it is using are really prime. In fact they all are because they are all very small. But when you tell IFAC to find small factors, even if it finds none, it declares the cofactors to be prime even though they probably aren't, and issues a warning at certain debug levels. Only after you have checked that the number is not obviously composite, e.g. divisible by a prime less than 1000 do you go through the full Pocklington test. Thus the full test only gets passed a number which is relatively likely to be prime in the first place and hence not a complete waste of time. Any number which then passes the Pocklington test is certainly prime. The only way a number can fail to get to the end of the test is if it is composite. Bill. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
