Strings of congruent primes in short intervals
نویسنده
چکیده
Fix > 0, and let p1 = 2, p2 = 3, . . . be the sequence of all primes. We prove that if (q, a) = 1, then there are infinitely many pairs pr, pr+1 such that pr ≡ pr+1 ≡ a mod q and pr+1 − pr < log pr. The proof combines the ideas of Shiu and of Goldston–Pintz–Yıldırım.
منابع مشابه
Bubbles of Congruent Primes
In [15], Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu’s theorem to imaginary quadratic fields, where we prove the existence of “bubbles” containing arbitrarily many primes which are all, up to units, congruent to a modulo q.
متن کاملA note on primes in short intervals
This paper is concerned with the number of primes in short intervals. We present a method to use mean value estimates for the number of primes in (x, x+x] to obtain the asymptotic behavior of ψ(x+x)−ψ(x). The main idea is to use the properties of the exceptional set for the distribution of primes in short intervals. Mathematics Subject Classification (2000). 11NO5.
متن کاملPrimes in Beatty Sequences in Short Intervals
In this paper we show that sieve methods used previously to investigate primes in short intervals and corresponding Goldbach type problems can be modified to obtain results on primes in Beatty sequences in short intervals.
متن کاملDifferent Stages, Different Signals: The Modulating Effect of Cognitive Conflict on Subsequent Processing
The present study used event-related potentials (ERPs) to investigate the function of signals induced by cognitive conflict during the detection stage and the resolution stage of perceptual processing. The study used a combination of the Stroop task and an affective priming task to examine the conflict priming effect when the stimulus onset asynchrony (SOA) was 200 ms or 800 ms. Behavioral resu...
متن کاملOn Congruent Primes and Class Numbers of Imaginary Quadratic Fields
We consider the problem of determining whether a given prime p is a congruent number. We present an easily computed criterion that allows us to conclude that certain primes for which congruency was previously undecided, are in fact not congruent. As a result, we get additional information on the possible sizes of Tate-Shafarevich groups of the associated elliptic curves. We also present a relat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. London Math. Society
دوره 84 شماره
صفحات -
تاریخ انتشار 2011