Problem 1761. Primes Faster for Large N

Created by Richard Zapor

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This Challenge is to improve the "primes" function for speed. This may be accomplished by fixing memory usage.The Matlab function "primes" has a very efficient sieving method but it suffers from a memory usage issue that may bump into a user's RAM size causing "out of memory", significant slow down, or Matlab freeze.Cody appears to have 2GB of RAM based upon "out of memory" messages observed.The test case of 2^28 starts to bump into memory limit affects but will complete with the standard primes function.The reference solution can process N=2^33 on a 16GB machine in 284sec.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 &lt; 2^28Hints:<pre class="language-matlab">1) Doubles use 8 bytes; logicals use 1 byte
2) The method p = p(p&gt;0); is good but can be improved
3) The method p = 1:2:n; creates a double and is a little slow
4) Usage of profiler and Task Manager combined give performance insights
</pre>Related: <a href = "http://www.mathworks.com/matlabcentral/cody/problems/1763-primes-for-large-n-2-30-system-memory-limit">Primes 2^30</a>Matlab 2014a incorporated the speed enhancement of logicals

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Last Solution submitted on Dec 31, 2020

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Richard Zapor on 7 Aug 2013

Bart crushed my 2^33 in 284 sec with a time of 92 sec.

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Problem 1761. Primes Faster for Large N

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Problem 1761. Primes Faster for Large N

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