Long chains of nearly doubled primes

Author:
Günter Löh

Journal:
Math. Comp. **53** (1989), 751-759

MSC:
Primary 11A41; Secondary 11Y11

DOI:
https://doi.org/10.1090/S0025-5718-1989-0979939-8

MathSciNet review:
979939

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Abstract: A chain of nearly doubled primes is an ordered set $\{ {a_1},{a_2}, \ldots ,{a_\lambda }\}$ of prime numbers, interlinked by ${a_k} = 2{a_{k - 1}} \pm 1$. A search for long chains of this kind has been performed in the range ${a_1} < {2^{50}}$. Chains of length up to 13 have been found. Shorter chains have been counted in some restricted ranges. Some of these counts are compared with the frequencies predicted by a quantitative version of the prime *k*-tuples conjecture.

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Additional Information

Keywords:
Nearly doubled primes,
prime chains,
Cunningham chains,
prime <I>k</I>-tuples conjecture

Article copyright:
© Copyright 1989
American Mathematical Society