X-x-1-x-2-x-n-X-P-n-Does-there-exist-a-point-in-N-dimensions-such-that-the-points-and-line-length-from-origin-are-prime-That-is-i-1-n-x-i-2-p-2-p-P-

Question Number 40974 by Penguin last updated on 30/Jul/18

$${X}\:=\:\left({x}_{\mathrm{1}} ,\:{x}_{\mathrm{2}} ,\:…,\:{x}_{{n}} \right),\:\:\:\:{X}\in\mathbb{P}^{{n}} \\ $$$$\: \\ $$$$\mathrm{Does}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{a}\:\mathrm{point}\:\mathrm{in}\:\mathrm{N}-\mathrm{dimensions}, \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{points}\:\mathrm{and}\:\mathrm{line}\:\mathrm{length}\:\left(\mathrm{from}\:\mathrm{origin}\right) \\ $$$$\mathrm{are}\:\mathrm{prime}? \\ $$$$\: \\ $$$$\mathrm{That}\:\mathrm{is}, \\ $$$$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{x}_{{i}} ^{\mathrm{2}} ={p}^{\mathrm{2}} ,\:\:\:{p}\in\mathbb{P} \\ $$

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