The code can only computed based on python 3.7.Python 3.9 and python 3.6 cannot compute the code.It is very strange problem.

What error are you getting?

Can you demonstrate the error without gmpy2, as that is a third-party library and nothing to do with us.

The issue is that if i use function pow(c,e),it can be computed in python37 in 3 minutes.But it cannot be computed in python36 or python39.Without gmpy2 library,i find the bug.

I cannot replicate that. On my computer, I can compute pow(c, e) in approximately two minutes using Python 3.9:


>>> from time import time
>>> t = time(); a = pow(c, e); time()-t
122.07566785812378
>>> math.log10(a)
50473921.44753242


Can you give more information please?

- exact version number used
- OS
- how much memory?
- if you leave pow(c, e) running for 10 minutes, does it complete?
- can you compute pow(c, 10000)? how long does that take?
- how about pow(c, 1000)?

Here are my information.
1.python 3.8.6
2.windows 10(build 19042 20h2)
3. 16Gb memory
4. It doesn't complete.It takes about 30 minutes but it gives no output.
5. It takes 6.346898794174194s
6. It takes 0.3690004348754883s.

Are you sure that this is a time of calculating pow() and not the time of calculating decimal representation of the result?

On my computer:

>>> t = time(); a = pow(c, 2**14+1); time()-t
11.957276344299316
>>> t = time(); a = pow(c, 2**15+1); time()-t
36.08853316307068
>>> t = time(); a = pow(c, 2**16+1); time()-t
107.43462753295898

The computational complexity is O((log(c)*e)**1.5). And it needs not so much memory: around 20 MB for final result, and few times more for intermediate results, so this is not matter of swapping.

ohhhhhhhhhhhhh.You are right.If i directly compute the huge result without printing,it only takes 115s.Thank you very much.I'm sorry to forget noting the print function.

The computational complexity of algorithm used to convert integer to decimals is proportional to the cube of the size of the number. It is known issue. There are better algorithms (perhaps gmpy2 uses them), but they benefit only extremely large numbers, for which exact decimal form is not very useful.