为什么外国的素数网站上这样表示？

素数粉

为什么外国的素数网站上
16生素数：
k=16  s=60  B={0  4  6  10  16  18  24  28  30  34  40  46  48  54  58  60}
               13  17  19  23  29  31  37  41  43  47  53  59  61  67  71  73
而不是
k=16  s=60  B={0  2  6  8  12  18  20  26  30  32  36  42  48  50  56  60}
               11  13  17  19  23  29  31  37  41  43  47  53  59  61  67  71

northwolves

与K-生素数的定义有关，见 http://mathworld.wolfram.com/PrimeConstellation.html

k consecutive numbers such that the difference between the first and last is, in some sense, the least possible. More precisely, a prime -tuplet is a sequence of consecutive primes (p1,p2,p3...pk ) with pk-p1=s(k), where s(k)  is the smallest number  for which there exist  k integers b1<b2<b3<...<bk,  bk-b1=s and, for every prime  q, not all the residues modulo  are represented by b1,b2,...bk(Forbes). For each , this definition excludes a finite number of clusters at the beginning of the prime number sequence. For example, (97, 101, 103, 107, 109) satisfies the conditions of the definition of a prime 5-tuplet, but (3, 5, 7, 11, 13) does not because all three residues modulo 3 are represented (Forbes).

northwolves

所以，当 k=16  s=60  B={0  2  6  12  14  20  26  30  32  36  42  44  50  54  56  60}

首素数最小的序列如下（http://anthony.d.forbes.googlepages.com/ktmin.txt）：
               47710850533373130107 + 0, 2, 6, 12, 14, 20, 26, 30, 32, 36, 42, 44, 50, 54, 56, 60  (1997, TF and Joerg Waldvogel)