How many different clock−type dials can be made containing first n natual numbers with the property that sum of any two numbers of consecutive positions be a prime number. N={1,2,3,...}


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Question Number 3172 by Rasheed Soomro last updated on 07/Dec/15

$H o w m a n y d i f f e r e n t c l o c k - t y p e d i a l s c a n b e m a d e$ $c o n t a i n i n g f i r s t n n a t u a l n u m b e r s w i t h t h e p r o p e r t y$ $t h a t s u m o f a n y t w o n u m b e r s o f c o n s e c u t i v e p o s i t i o n s b e$ $a p r i m e n u m b e r .$ $N = {1, 2, 3, . . .}$
Commented by Rasheed Soomro last updated on 07/Dec/15

$F o r n = 1 t h e r e i s n o s u c h d i a l .$ $F o r n = 2 t h e r e i s 1 s u c h d i a l .$ $F o r n = 3 t h e r e i s n o s u c h d i a l .$ $F o r n = 4 t h e r e a r e t w o s u c h d i a l s : 12341, 14321$ $F o r n = 5 :$ $⋮$ $F o r n t h e r e a r e m s u c h d i a l s . W h a t i s m ?$
	Answered by prakash jain last updated on 06/Dec/15

	$No such formula is possible due to the fact that$ $there is no formula for prime numbers .$
	Commented by Rasheed Soomro last updated on 07/Dec/15

	$A n y i m p o s s i b i l i y f o r s o m e t y p e o f n u m b e r s ? F o r$ $e x a m p l e f o r o d d n u m b e r s e t c ?$
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