What is the smallest even number greater than 3 that cannot be expressed as the sum of two prime numbers ?


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Question Number 6772 by Tawakalitu. last updated on 24/Jul/16

$W h a t i s t h e s m a l l e s t e v e n n u m b e r g r e a t e r t h a n 3 t h a t c a n n o t$ $b e e x p r e s s e d a s t h e s u m o f t w o p r i m e n u m b e r s ?$
Commented by Yozzii last updated on 24/Jul/16

$L e t S b e a s e t o f n e l e m e n t s, s o t h a t ∣ S ∣= n ⩾ 4 .$ $L e t P b e a p a r t i t i o n o f S i n t o t w o s e t s$ $X, Y s u c h t h a t X \cap Y = \emptyset a n d S = X \cup Y .$ $I s t h e r e a p a r i t i t i o n P s u c h t h a t a t l e a s t o n e$ $o f ∣ X ∣ a n d ∣ Y ∣ m u s t b e c o m p o s i t e, a n d 2 ∣ n ?$ $W h a t i s m i n (n) ?$
Commented by Tawakalitu. last updated on 24/Jul/16

$T h a n k s f o r y o u r h e l p .$
Commented by prakash jain last updated on 25/Jul/16

$Small even number = 4 = 2 + 2$
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