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Let \ \ p_n \ \ = \ \ the \ \ nth \ \ prime \ \ number.Examples:p_1 \ = \ 2
p_2 \ = \ 3
p_3 \ = \ 5
p_4 \ = \ 7- - - - - - - - - - - - - - - - - - - - - - - - - - - - Let \ \ n \ \ belong \ \ to \ \ the \ \ set \ \ of \ \ positive \ \ integers.
Prove (or disprove) the following:p_n \ + \ p_{n + 1} \ \ \ge \ \ p_{n + 2} \ + \ p_{n - 2}, \ \ \ for \ \ all \ \ n \ \ge \ 4.Examples:\ \ 7 \ + \ 11 \ \ > \ \ 13 \ + \ \ 3
19 \ + \ 23 \ \ = \ \ 29 \ + \ 13
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Let \ \ p_n \ \ = \ \ the \ \ nth \ \ prime \ \ number.Examples:p_1 \ = \ 2
p_2 \ = \ 3
p_3 \ = \ 5
p_4 \ = \ 7- - - - - - - - - - - - - - - - - - - - - - - - - - - - Let \ \ n \ \ belong \ \ to \ \ the \ \ set \ \ of \ \ positive \ \ integers.
Prove (or disprove) the following:p_n \ + \ p_{n + 1} \ \ \ge \ \ p_{n + 2} \ + \ p_{n - 2}, \ \ \ for \ \ all \ \ n \ \ge \ 4.Examples:\ \ 7 \ + \ 11 \ \ > \ \ 13 \ + \ \ 3
19 \ + \ 23 \ \ = \ \ 29 \ + \ 13
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