7

This number is a prime.

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The only prime that can be the digital root (sum of digits computed recursively until one digit remains) of a perfect square. [Rupinski]

The dimensions of irreducible modules of the exceptional Lie group G_2 are all congruent to {-1,0,+1} mod 7. A similar phenomenon occurs for all exceptional Lie groups and for some classical ones as well. [Rupinski]