Prime sieve optimization

#1

i am not understand 4th approach of optimization please explain

#2

hello @vishal_sangal_123

its property that if number is n then atleast one of its prime factors lie sqrt(n).

so if i*i is the number then one of prime factor will lie in range i.

so that is the reason if we are at i then we are starting from ii onwards.
becuase all elements that are less than ii are already marked by prime factor less than i