科研之友
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摘要
For a set D of positive integers, a sequence {a(1) < a(2) < ... < a(k)} is called an k-term D-diffseguence if a(i) - a(i-1) is an element of D for all i is an element of {2,..., k). For a positive integer r, a set of positive integers D is r-accessible if every r-coloring of Z(+) has arbitrarily long monochromatic D-diffsequences. The largest r such that D is r-accessible is called the degree of accessibility of D. It is already known that each odd translation of the set of primes, P + t, is 2-accessible. We offer new results on the accessibility of translations the primes. The main result is that for any c >= 2, the degree of accessibility of P + c does not exceed the smallest prime factor of c.
- 出版日期2010-7
