|
Oppermann's conjecture is an unsolved problem in mathematics on the distribution of prime numbers.〔.〕 It is closely related to but stronger than Legendre's conjecture, Andrica's conjecture, and Brocard's conjecture. It is named after Danish mathematician Ludvig Oppermann, who posed it in 1882. ==Statement== The conjecture states that, for every integer ''x'' > 1, there is at least one prime number between : ''x''(''x'' − 1) and ''x''2, and at least another prime between : ''x''2 and ''x''(''x'' + 1). It can also be phrased equivalently as stating that the prime-counting function must take unequal values at the endpoints of each range.〔.〕 That is: : ''π''(''x''2 − x) < ''π''(''x''2) < ''π''(''x''2 + ''x'') for ''x'' > 1 with ''π''(''x'') being the number of prime numbers less than or equal to ''x''. The end points of these two ranges are a square between two pronic numbers, with each of the pronic numbers being twice a pair triangular number. The sum of the pair of triangular numbers is the square. 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「Oppermann's conjecture」の詳細全文を読む スポンサード リンク
|