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Absolute prime numbers

Published online by Cambridge University Press:  01 August 2016

Dmitry Mavlo
Dmitry Mavlo*
Affiliation:
125195, Moscow, Fyestivalnaya 25-64, Russia
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Extract

For a long time prime numbers have attracted the attention of mathematicians, especially those primes that possess some sort of a symmetry. The mysterious repunits An = 111… 1(n), whose decimal representations contain only units, form an important class of them. For a repunit to be prime the number n of its digits must be also prime. But this condition is far from being sufficient: for instance, A3 = 111 = 3.37 and A5 = 11111 = 41.271. Some of the repunits are nonetheless prime: A2, A19, A23, A317 and A1031, are the only known examples. The question of primeness of the repunits was discussed by M. Gardner and later in [2–4]. It is not clear whether the number of prime repunits is finite or infinite.

Type
Articles
Information
The Mathematical Gazette , Volume 79 , Issue 485 , July 1995 , pp. 299 - 304
Copyright
Copyright © The Mathematical Association 1995

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References

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