PDF(345 KB)
PDF(345 KB)
PDF(345 KB)
Terence Tao的一个问题
On a Problem of Terence Tao
解决了Terence Tao提出的一个问题.证明了:设K ≥ 2,N充分大, LN为{-KN,…, KN}的任意子集, |LN|=K.那么在[N,(1+1/K)N]中至少存在CKN/log N个素数p,使得|kp+jai+l|为合数,其中1 ≤ a,|j|,k ≤ K, 1 ≤ i ≤ K log N, l∈LN, jai+l≠0,常数CK>0与K有关.
We solve a problem of Terence Tao. We prove that for any K≥2 and sufficiently large N, the number of primes p between N and (1+1/K)N such that |kp+jai+l| is composite for all 1≤a, |j|, k≤K, 1 ≤ i ≤ K log N and l in any set LN⊆{-KN, …, KN} of cardinality K with jai+l≠0 is at least CK M/log N, where CK>0 depending only on K.
Terence Tao问题 / 素数 / Selberg筛法 {{custom_keyword}} /
Terence Tao's problem / primes / Selberg's sieve method {{custom_keyword}} /
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国家自然科学基金资助项目(11471017);淮海工学院自然科学基金资助项目(KQ10002)
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