> comp.lang.python is a good place to get answers about Python. It's > probably not such a good source of answers about computational number > theory. Also, Python is more about productivity than speed, so > answers involving Python may not be the most efficient possible > answers. One obvious point though is that GMP/gmpy is pretty simple > to use from Python and will be several times faster than Python's > built in longs. Also, as Mensanator pointed out, GMP has built-in > functions that will help you with precise checks (I'd forgotten or not > known about them). I still think you'd get a speedup from first > filtering out obviously non-square candidates before resorting to > multi-precision arithmetic. Some other fairly simple optimization may > be possible too. > gmpy.is_square() is quite fast. On a older 32-bit Linux box, it can test approximately 400,000 100-digits numbers per second. The time includes conversion from a string. If the numbers are already Python longs, it can check 800,000 per second. Checking a billion is not unreasonable.
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