Comment #22 on issue 1827 by smi...@gmail.com: log eval gives more standard
form
http://code.google.com/p/sympy/issues/detail?id=1827
Well, ya got lucky and sympy improved because of it! From what I've learned,
a more deterministic way of doing it would be to pick a large prime, p, out
of the 2**15 range and then pick another that is more than sqrt(p) away,
preferably p away, and then the product shouldn't be so easily factored with
trial division (at least). If the second prime is within sqrt(p) then
factors will be found as easily with the relatively quick Fermat test as the
small factors are found with trial division. So...p = nextprime(2**30); p *=
nextprime(2*p) should give a small(er) p that is hard to factor with trial
division. Starting from 2**24 gives a slight delay...2**25 gives a
significant delay. 2**30 would be big enough to write a test that would
appear to hang
The thing is, the special methods can find a factor if it's is sitting *next
to* something that has special properties. So that prime made starting with
primes past 2**30 factors in less than 2 seconds. So if you employ the
special methods you're going to be able to handle much larger input...at the
risk of getting hung up by the rarer strong pseudoprime. While writing this
I have had a loop running:
>>> for i in range(25,60):
... p=nextprime(2**i);p*=nextprime(2*p);print i, p, factorint(p)
i = 41 took a long time and 42 is taking a long time. So perhaps I should
add one of these into the tests.
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