Which is not a Sieve! But then the OP's proposal is neither...

Update: this is a sieve (specify sieve size on command line):

$_=";"x(pop);s;.;.;;$;=~s:.:.:g,s:($;).:$1.:g,s,($;).,$1:,while($;)=m:
+(.+?);:;s;:;1+pos();ge;say
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