The differences between consecutive smooth numbers

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the Difference between Consecutive Ramsey Numbers

It is shown that the classical Ramsey numbers T( m, ta) satisfy r(m,n) 2: r(m,n1) + 2m3,

متن کامل

Large Gaps between Consecutive Prime Numbers

Let G(X) denote the size of the largest gap between consecutive primes below X . Answering a question of Erdős, we show that G(X) > f(X) logX log logX log log log logX (log log logX) , where f(X) is a function tending to infinity with X . Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the e...

متن کامل

A Note on the Distribution of Differences between Consecutive Prime Numbers

A Note on The Distribution of Differences Between Consecutive Prime Numbers Lester D. Taylor University of Arizona The results reported in this note refer to the distribution of zn = pn pn-1 for the first three million prime numbers (p). The analyses of the note are almost purely statistical. The difference between consecutive prime numbers is treated as a random variable, and empirical frequen...

متن کامل

On the Distance between Smooth Numbers

Let P (n) stand for the largest prime factor of n ≥ 2 and set P (1) = 1. For each integer n ≥ 2, let δ(n) be the distance to the nearest P (n)-smooth number, that is, to the nearest integer whose largest prime factor is no larger than that of n. We provide a heuristic argument showing that � n≤x 1/δ(n) = (4 log 2 − 2 + o(1))x as x → ∞. Moreover, given an arbitrary real-valued arithmetic functio...

متن کامل

On Consecutive Happy Numbers

Let e > 1 and b > 2 be integers. For a positive integer n = ∑k j=0 aj × b j with 0 6 aj < b, define

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Acta Arithmetica

سال: 2018

ISSN: 0065-1036,1730-6264

DOI: 10.4064/aa170913-11-7