Joseph Farah - 6 months ago 9

Python Question

I have a prime number generator, I was curious to see how small and how fast I could get a prime number generator to be based on optimizations and such:

`from math import sqrt`

def p(n):

if n < 2: return []

s = [True]*(((n/2)-1+n%2)+1)

for i in range(int(sqrt(n)) >> 1):

if not s[i]: continue

for j in range( (i**i+(3*i) << 1) + 3, ((n/2)-1+n%2), (i<<1)+3): s[j] = False

q = [2]; q.extend([(i<<1) + 3 for i in range(((n/2)-1+n%2)) if s[i]]); return len(q), q

print p(input())

The generator works great! It is super fast, feel free to try it out. However, if you input numbers greater than 10^9 or 10^10 (i think) it will crash from a memory error. I can't figure out how to expand the memory it uses so that it can take as much as it needs. Any advice would be greatly appreciated!

My question is very similar to this one, but this is Python, not C.

EDIT: This is one of the memory related tracebacks I get for trying to run 10^9.

`python prime.py`

1000000000

Traceback (most recent call last):

File "prime.py", line 9, in <module>

print p(input())

File "prime.py", line 7, in p

for j in range( (i**i+(3*i) << 1) + 3, ((n/2)-1+n%2), (i<<1)+3): s[j] = False

MemoryError

Answer

The Problem is in line 7.

```
for j in range( (i**i+(3*i) << 1) + 3, ((n/2)-1+n%2), (i<<1)+3): s[j] = False
```

especially this part: `i**i`

1000000000^1000000000 is a 9 * 10^9 digit long number. Storing it takes multiple Gb if not Tb (WolframAlpha couldn't caclulate it anymore). I know that i ist the square root of n (maximal), but at that large numbers that's not a big difference.

You have to split this caclulation into smaller parts if posible and safe it on a hard drive. This makes the process slow, but doable.