# Lemon and melon

Number Theory Level 4

In a two-dimensional plane there are some vectors. We call a vector as a lemon vector if it has positive integer coordinates, and we call a vector a melon vector if its coordinates are primes.

We know that $$\overrightarrow { u }$$, $$\overrightarrow{ v }$$ and $$\overrightarrow { w }$$ are three lemon vectors, and $$\overrightarrow { u+v }$$, $$\overrightarrow { v+w }$$ and $$\overrightarrow{ w+u }$$ are three melon vectors. How many different $$\overrightarrow { v }$$ vectors there are if $$\overrightarrow { u }$$, $$\overrightarrow { v }$$ and $$\overrightarrow { w }$$ have the same angle but different module?

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