The Prime Life of Hexagon Flowers

Equilateral hexagons can be put together in a flower-like way:

From the picture above you can clearly see that 7 hexagons are necessary to built a "two-row"-flower. If we built a three row flower, 19 hexagons are needed.
7 and 19 are both primes. If we add more rows will we ever be able to make a hexagon-flower with a non-prime total amount of hexagons?

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