Unexpected biases in the distribution of consecutive primes.
نویسندگان
چکیده
Although the sequence of primes is very well distributed in the reduced residue classes [Formula: see text], the distribution of pairs of consecutive primes among the permissible ϕ(q)(2) pairs of reduced residue classes [Formula: see text] is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared with numerical data, and the observed fit is very good.
منابع مشابه
Unexpected Biases in the Distribution of Consecutive Primes
While the sequence of primes is very well distributed in the reduced residue classes (mod q), the distribution of pairs of consecutive primes among the permissible φ(q) pairs of reduced residue classes (mod q) is surprisingly erratic. This paper proposes a conjectural explanation for this phenomenon, based on the Hardy-Littlewood conjectures. The conjectures are then compared to numerical data,...
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ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 113 31 شماره
صفحات -
تاریخ انتشار 2016