Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly i...Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly in k,and every prime divides all sufficiently large most likely common differences.展开更多
文摘Let d^(∗)_(k)(x)be the most likely common differences of arithmetic progressions of length k+1 among primes≤x.Based on the truth of Hardy–Littlewood Conjecture,we obtain that lim x→+∞d^(∗)_(k)(x)(x)=+∞uniformly in k,and every prime divides all sufficiently large most likely common differences.
