Python-prime-number-generator-optimization-

Python script to generate first n prime numbers . Optimized by levels . Detailed time and optimization info given

The various optimizations done in each level are:

v1 - no optimization
v2 - added break
v3 - filter out even
v4 - filter out even in for loop directly
v5 - limit search to half of i
v6 - limit search to square root of i
v7 - limit search to only previous prime numbers
v8 - limit search to only previous prime numbers but checking for less than directly at list addition rather than during modulus check
v9 - taking finding of sqrt of final number as constant outside
v10 - minor fixes
v11 - implementing sieve method?
v12 - optimised version of sieve check ( multiples of 2 removed during set creation )

Their respective time required are:

258.44545817375183    
24.8780837059021   
23.12345814704895   
22.465441465377808  
11.63539743423462    
0.11180853843688965   
0.09911322593688965   
0.03931570053100586   
0.03710675239562988   
0.020193815231323242  
0.015111684799194336