maximum integer length?

[mensanator at aol.com]

nate wrote:
> Hey everyone,
>
> I am trying to figure out what is the largest integer I can. Lets say
> for 400 megabytes of memory at my disposal.
>
> I have tried a few things
> c = 2**1000000
> d = 2**2000000
> print c**d
>
> Obviously I didn't have enough memory for that, but I was able to c**3.
> (I think anyways, it is still trying to display the result)

Don't print, takes too long. Do e=c**3.

>
> So I am just wondering how long an integer can be with 400 megabytes of
> memory.
>
> I guess this is a question of logic?
> each integer takes up a byte right? If I have 400 megabytes that would
> mean I could have a long integer with up to 419,430,400,000 integers?
>
> Really I am not sure on this one and that is why I am asking. Because it
> is just bugging me I am not sure how it works...
>
> I know this probably seems trivial and just a stupid question, but I
> find this type of stuff interesting...

Using gmpy (and I don't know if it stores large ints different
from Python ints) and only 192M on my laptop, I can get
to billion bit numbers, but not much larger. Switching to
Python ints ran out of memory trying gen 11. It also ran out
of memory trying to calculate gen 10, which gmpy was able
to do successfully, so maybe gmpy is better for such things:

Closed form: Type12MH(k,i)
Find ith, kth Generation Type [1,2] Mersenne Hailstone
using the closed form equation

2**(6*((i-1)*9**(k-1)+(9**(k-1)-1)/2+1)-1)-1

            2**5-1  generation: 1
           2**29-1  generation: 2
          2**245-1  generation: 3
         2**2189-1  generation: 4
        2**19685-1  generation: 5
       2**177149-1  generation: 6
      2**1594325-1  generation: 7
     2**14348909-1  generation: 8
    2**129140165-1  generation: 9
   2**1162261469-1  generation:10

Traceback (most recent call last):
  File "C:\python24\user\user_home\gmpy ver 1.01\MHtest.py", line 41,
in -toplevel-
    a = Type12MH(k,1)
  File "C:\python24\lib\collatz_functions.py", line 595, in Type12MH
    return TWO**(SIX*a - ONE) - ONE
ValueError: mpz.pow outrageous exponent


>>>
>>> i=1
>>> k=11
>>> a = 2**(6*((i-1)*9**(k-1)+(9**(k-1)-1)/2+1)-1)-1

Traceback (most recent call last):
  File "<pyshell#3>", line 1, in -toplevel-
    a = 2**(6*((i-1)*9**(k-1)+(9**(k-1)-1)/2+1)-1)-1
MemoryError