# Derek's prime-tuple

Number Theory Level 5

How many distinct $$4$$-tuples of (positive) primes $$(p_1, p_2, p_3, p_4)$$ are there such that $$p_1 < p_2 < p_3 < p_4$$ and

$p_1^2 + p_2^2 + p_3^2 + p_4^2 = 2223?$

This problem is posed by Derek K.

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