Is cubic a prime?

x344x2+556x1805\Large x^3-44x^2+556x-1805

Let x1,x2,x3,xnx_1,x_2,x_3,\dots x_n be the positive integers that make the above expression a (positive) prime number. Then, find the value of i=1nxi \displaystyle \sum_{i=1}^n x_i .

Also try Is Quartic a square?
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