|
The number 2,147,483,647 (two billion, one hundred and forty-seven million, four hundred and eighty-three thousand, six hundred and forty-seven) is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.〔.〕 The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Bernoulli written in 1772.〔.〕 Euler used trial division, improving on Cataldi's method, so that at most 372 divisions were needed.〔.〕 It thus improved upon the previous record-holding prime, 6,700,417, also discovered by Euler, forty years earlier. The number 2,147,483,647 remained the largest known prime until 1855.〔.〕 ==Barlow's prediction== In 1811, Peter Barlow, not anticipating future interest in prime numbers, wrote (in (''An Elementary Investigation of the Theory of Numbers'' )): Euler ascertained that 231 − 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers (230(231 − 1) ), which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for as they are merely curious, without being useful, it is not likely that any person will attempt to find one beyond it. He repeated this prediction in his 1814 work (''A New Mathematical and Philosophical Dictionary'' ).〔.〕〔.〕 In fact a larger prime was discovered in 1855 by Thomas Clausen (67,280,421,310,721), though a proof was not provided. Furthermore, 3,203,431,780,337 was proven to be prime in 1867. 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「2147483647 (number)」の詳細全文を読む スポンサード リンク
|