|
A prime quadruplet (sometimes called prime quadruple) is a set of four primes of the form .〔 Retrieved on 2007-06-15.〕 This represents the closest possible grouping of four primes larger than 3. == Prime quadruplets == The first prime quadruplets are: , , , , , , , All prime quadruplets except are of the form for some integer ''n''. (This structure is necessary to ensure that none of the four primes is divisible by 2, 3 or 5). A prime quadruplet of this form is also called a prime decade. A prime quadruplet contains two pairs of twin primes or can be described as having two overlapping prime triplets. It is not known if there are infinitely many prime quadruplets. A proof that there are infinitely many would imply the twin prime conjecture, but it is consistent with current knowledge that there may be infinitely many pairs of twin primes and only finitely many prime quadruplets. The number of prime quadruplets with ''n'' digits in base 10 for ''n'' = 2, 3, 4, ... is 1, 3, 7, 26, 128, 733, 3869, 23620, 152141, 1028789, 7188960, 51672312, 381226246, 2873279651 . the largest known prime quadruplet has 3503 digits.〔(''The Top Twenty: Quadruplet'' ) at The Prime Pages. Retrieved on 2013-12-23.〕 It starts with ''p'' = 2339662057597 × 103490 + 1. The constant representing the sum of the reciprocals of all prime quadruplets, Brun's constant for prime quadruplets, denoted by ''B''4, is the sum of the reciprocals of all prime quadruplets: : with value: :''B''4 = 0.87058 83800 ± 0.00000 00005. This constant should not be confused with the Brun's constant for cousin primes, prime pairs of the form (''p'', ''p'' + 4), which is also written as ''B''4. The prime quadruplet is alleged to appear on the Ishango bone although this is disputed. Excluding the first prime quadruplet, the shortest possible distance between two quadruplets and is ''q'' - ''p'' = 30. The first occurrences of this are for ''p'' = 1006301, 2594951, 3919211, 9600551, 10531061, ... (). 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「prime quadruplet」の詳細全文を読む スポンサード リンク
|