Sieve of Eratosthenes, Step by Step
Jelly, 34 bytes

Ṿ€“1“ ”ys³G
&gt;®i©1ḍoṛ®¦
²R;1©ÇÐĿÑ€Y


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How it works

²R;1©ÇÐĿÑ€Y  Main link. Argument: n (integer)

²            Yield n².
 R           Range; yield [1, ..., n²].
   1©        Yield 1 and copy it to the register.
  ;          Append 1 to the range.
             This is the initial state. Let's call it S.
     ÇÐĿ     Call the second helper link until the results are no longer unique.
             This returns all unique results as an array.
        Ṅ€   Call the first helper link on each result.
          Y  Join, separating by linefeeds.

&gt;®i©1ḍoṛ®¦   Second helper link. Argument: S (state)

&gt;®           Compare all integers in S with the value in the register.
  i 1        Find the first index of 1 (i.e., the first number that is greater
             than the register.
   ©         Copy the index to the register. Let's call the index p.
     ḍ       Test all numbers in S for divisibility by p. This yield 1 for
             multiples of p, 0 otherwise.
      o      Logical OR; replace 0's with the corresponding values of S.
       ṛ®¦   Replace the 0 at index p with the corresponding element of S (p).
             For the purposes of the explanation, S is now the updated state.

Ṿ€“1“ ”ys³G  First helper link. Argument: A (array)

Ṿ€           Uneval each; convert all integers in A into strings.
  “1“ ”y     Replace each string "1" with the string " ".
        s³   Split into chunks of length n (command-line argument).
          G  Grid; separate row items by spaces (left-padding since the row items
             are strings), the rows themselves by linefeeds.