Sum prime

Is it possibe to write down the 1 , 2 , 3 , , 100 1, 2, 3, \dots, 100 numbers in some order (one after an other), such that the sum of any two adjacent numbers is a prime number?

No, it is not possible Yes, it is possible

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1 solution

Áron Bán-Szabó
Aug 16, 2017

Here is an example: 1 , 100 , 3 , 98 , , 97 , 4 , 99 , 2 {\color{#D61F06}{1}}, {\color{#3D99F6}{100}}, {\color{#D61F06}{3}}, {\color{#3D99F6}{98}}, \dots, {\color{#D61F06}{97}}, {\color{#3D99F6}{4}}, {\color{#D61F06}{99}}, {\color{#3D99F6}{2}} Now the sum of any two adjacent numbers is ether 101 or 103. The red {\color{#D61F06}{\text{red}}} numbers are the odd numbers in a increasing order and the blue {\color{#3D99F6}{\text{blue}}} numbers are the even numbers in a decreasing order.

Ah, very clever! :)

Geoff Pilling - 3 years, 9 months ago

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