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Problem 1763. Primes for Large N: 2^30, System Memory Limit

Created by Richard Zapor

This Challenge is to further improve the "primes" function for speed/memory usage to the Limit of Cody Memory.

The Matlab function "primes" has a very efficient sieving method but it suffers from memory usage issues, especially on limited memory systems.

The Primes Faster Challenge gives the first half to maximizing the primes function for optimal memory usage and speed.

Cody appears to have 2GB of RAM based upon "out of memory" messages observed.

The test case of 2^30 pushes the upper limits of Cody memory.

The reference solution can process N=2^32 on an 8GB machine in 68sec.

Input: N (max of primes to find)

Output: vector of primes (all primes less than or equal to N)

Scoring: Time to find all primes < 2^30

Hints:

1) Doubles use 8 bytes;
2) The primes method  p(((k*k+1)/2):k:q) creates a vector using q/k*8 bytes. This is 8/3 the size of p for k=3 because k is a double. 
3) Segmentation will keep memory usage below limits at the cost of time.
4) Cody Available Memory appears to be 537.27MB. XP Operating system eats memory.
5) Usage of profiler and Task Manager combined give performance insights.

Problem Group

Solution Statistics

10 correct solutions 14 incorrect solutions
Last solution submitted on Aug 14, 2014

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