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Question Number 189970 by Rupesh123 last updated on 25/Mar/23

	Answered by Rasheed.Sindhi last updated on 25/Mar/23

	$x, y, x + y, x - y \in P; x, y = ?$ $∙ I f x a n d y w e r e b o t h o d d p r i m e s$ $\Rightarrow 2 ∣ (x + y) \Rightarrow x + y \notin P o r x + y = 2$ $x + y = 2 h a s n o s o l u t i o n i n p r i m e$ $∙ I f x = y = 2 \Rightarrow x + y, x - y \notin P$ $H e n c e o n e o f x a n d y i s e v e n p r i m e$ $a n d t h e o t h e r i s o d d p r i m e .$ $∙ A s s u m i n g x - y > 0 \Rightarrow y = 2$ $∙ x + 2, x, x - 2 a r e t w i n p r i m e s (h a v i n g$ $d i f f e r e n c e 2)$ $∙ O n l y t h r e e c o n s e c u t i v e t w i n p r i m e s a r e$ $3, 5, 7$ $x + 2 = 7, x = 5, x - 2 = 3$ $∙ x = 5, y = 2$
	Commented by Rupesh123 last updated on 25/Mar/23
	Excellent!
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