It's got funny symbols, so I assume APL. [1]

[1] https://en.wikipedia.org/wiki/APL_(programming_language)

It's an APL sieve, for an input of 15 (primes up to 15) it does these steps:

First 15 integers:

          ⍳ 15
    ┌→──────────────────────────────────┐
    │1 2 3 4 5 6 7 8 9 10 11 12 13 14 15│
    └~──────────────────────────────────┘

1 element dropped from the front of that:

          1↓⍳15
    ┌→────────────────────────────────┐
    │2 3 4 5 6 7 8 9 10 11 12 13 14 15│
    └~────────────────────────────────┘

That array stored in variable T:

          T←1↓⍳15

A table of outer-product multiplication, T by T:

          T∘.×T
    ┌→─────────────────────────────────────────────────┐
    ↓ 4  6  8 10 12  14  16  18  20  22  24  26  28  30│
    │ 6  9 12 15 18  21  24  27  30  33  36  39  42  45│
    │ 8 12 16 20 24  28  32  36  40  44  48  52  56  60│
    │10 15 20 25 30  35  40  45  50  55  60  65  70  75│
    │12 18 24 30 36  42  48  54  60  66  72  78  84  90│
    │14 21 28 35 42  49  56  63  70  77  84  91  98 105│
    │16 24 32 40 48  56  64  72  80  88  96 104 112 120│
    │18 27 36 45 54  63  72  81  90  99 108 117 126 135│
    │20 30 40 50 60  70  80  90 100 110 120 130 140 150│
    │22 33 44 55 66  77  88  99 110 121 132 143 154 165│
    │24 36 48 60 72  84  96 108 120 132 144 156 168 180│
    │26 39 52 65 78  91 104 117 130 143 156 169 182 195│
    │28 42 56 70 84  98 112 126 140 154 168 182 196 210│
    │30 45 60 75 90 105 120 135 150 165 180 195 210 225│
    └~─────────────────────────────────────────────────┘

The elements of T which exist (are found) in the multiplication table, boolean result:

          T∊T∘.×T
    ┌→──────────────────────────┐
    │0 0 1 0 1 0 1 1 1 0 1 0 1 1│
    └~──────────────────────────┘

Showing that together with the input, 4 6 8 are found, 2 3 5 are not:

          T,[0.5]T∊T∘.×T
    ┌→────────────────────────────────┐
    ↓2 3 4 5 6 7 8 9 10 11 12 13 14 15│
    │0 0 1 0 1 0 1 1  1  0  1  0  1  1│
    └~────────────────────────────────┘
    

Numbers not found in the multiplication table are prime, so invert the test result so primes get 1 and composites get 0:

    ~T∊T∘.×T
    ┌→──────────────────────────┐
    │1 1 0 1 0 1 0 0 0 1 0 1 0 0│
    └~──────────────────────────┘
    

Use that to 'compress' the input to keep things where the 1 positions are and drop things where the 0s are:

          (~T∊T∘.×T)/T
    ┌→────────────┐
    │2 3 5 7 11 13│
    └~────────────┘

You can play with it at https://tryapl.org/ using the bar at the top to enter the symbols.