素数粉 发表于 2009-2-3 23:34:03

为什么外国的素数网站上这样表示?

为什么外国的素数网站上
16生素数:
k=16s=60B={04610161824283034404648545860}
               13171923293137414347535961677173
而不是
k=16s=60B={0268121820263032364248505660}
               11131719232931374143475359616771

northwolves 发表于 2009-2-4 21:23:31

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 numberfor which there existk integers b1<b2<b3<...<bk,bk-b1=s and, for every primeq, not all the residues moduloare 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 发表于 2009-2-4 21:28:57

所以,当 k=16s=60B={02612142026303236424450545660}

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)
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