Primes in tuples III: On the difference {$p_{n + \nu}- p_n$}
نویسندگان
چکیده
منابع مشابه
Primes in tuples I
We introduce a method for showing that there exist prime numbers which are very close together. The method depends on the level of distribution of primes in arithmetic progressions. Assuming the Elliott-Halberstam conjecture, we prove that there are infinitely often primes differing by 16 or less. Even a much weaker conjecture implies that there are infinitely often primes a bounded distance ap...
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is greater than (c2/2)n. A simple calculation now shows that the primes satisfying (4) also satisfy the first inequality of (3) i΀ = e(ci) is chosen small enough. The second inequality of (3) is proved in the same way, which proves Theorem 2. Further, we obtain, as an immediate corollary of Theorem 1, that Received by the editors October 17, 1947. 1 P. Erdös and P. Turân, Some new questions on...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2006
ISSN: 0208-6573
DOI: 10.7169/facm/1229442618