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Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics. It states: :Every even integer greater than 2 can be expressed as the sum of two primes. The conjecture has been shown to hold up through 4 × 1018,〔("Goldbach conjecture verification" )〕 but remains unproven despite considerable effort. == Goldbach number == A Goldbach number is a positive integer that can be expressed as the sum of two odd primes.〔 Therefore, another statement of Goldbach's conjecture is that all even integers greater than 4 are Goldbach numbers. The expression of a given even number as a sum of two primes is called a Goldbach partition of that number. The following are examples of Goldbach partitions for some even numbers: :4 = 2 + 2 :6 = 3 + 3 :8 = 3 + 5 :10 = 3 + 7 = 5 + 5 :12 = 7 + 5 :... :100 = 3 + 97 = 11 + 89 = 17 + 83 = 29 + 71 = 41 + 59 = 47 + 53 :... The number of ways in which 2''n'' can be written as the sum of two primes (for ''n'' starting at 1) is: :0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 4, 4, 2, 3, 4, 3, 4, 5, 4, 3, 5, 3, 4, 6, 3, 5, 6, 2, 5, 6, 5, 5, 7, 4, 5, 8, 5, 4, 9, 4, 5, 7, 3, 6, 8, 5, 6, 8, 6, 7, 10, 6, 6, 12, 4, 5, 10, 3, ... . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Goldbach's conjecture」の詳細全文を読む スポンサード リンク
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