algorithm Sieve of Eratosthenes is

input: an integer nn $>1.$

output: all prime numbers from $2$ through n$.$

let A be an array of Boolean values, indexed by integers $2$ to nn$,$

initially all set to true.

for i $=2,3,4,...,$ not exceeding $$nn do

if A$[$i$]$ is true

for j $=$ i$2,$ i$2+$i$,$ i$2+2$i$,$ i$2+3$i$,...,$ not exceeding n do

set A$[$j$]$ :$=$ false

return all i such that A$[$i$]$ is true.