The roots of the polynomial \[x^3 - 52x^2 + 581x - k\]are distinct prime numbers. Find $k.$
<|im_start|>system
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<|im_start|>user
The roots of the polynomial \[x^3 - 52x^2 + 581x - k\]are distinct prime numbers. Find $k.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

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The roots of the polynomial \[x^3 - 52x^2 + 581x - k\]are distinct prime numbers. Find $k.$
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