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Yes, yes, aliens again...

the question

... so, what is the next row in this aperiodic table of alien elements?

(To save you from drawing and uploading an image to answer the question, 25 possibilities follow. 5 are the elements in question, and the other 20 are not elements. Which 5, and in what order? I put a spoiler tag on them since they are a minor hint, you may wish to try to answer the question without looking at them.)

possible answers

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I believe the answer is

D4, A4, C4, C3, A2

Explained:

Each element represents the prime numbers. For example, the top-left one represents 2, the next represents 3, etc.

To calculate the representation for a given prime number, subtract 1 and find the prime factorisation of that number. Then take the representations of those factors and put them inside the circle.

26th prime is 101: 101 - 1 = 100 = 2 * 2 * 5 * 5 = D4
27th prime is 103: 103 - 1 = 102 = 2 * 3 * 17 = A4
28th prime is 107: 107 - 1 = 106 = 2 * 53 = C4
29th prime is 109: 109 - 1 = 108 = 2 * 2 * 3 * 3 * 3 = C3
30th prime is 113: 113 - 1 = 112 = 2 * 2 * 2 * 7 = A2

[and here's the picture --OP]

D4 A4 C4 C3 A2

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  • 1
    $\begingroup$ Well done, and welcome! $\endgroup$ – deep thought Sep 27 '18 at 4:46

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