Broughan, K. A. & Zhou, Q. (2010). Flat primes and thin primes. Bulletin of the Australian Mathematical Society, 82(2), 282-292.
Permanent Research Commons link: http://hdl.handle.net/10289/4780
A number is called upper (lower) flat if its shift by +1 ( −1) is a power of 2 times a squarefree number. If the squarefree number is 1 or a single odd prime then the original number is called upper (lower) thin. Upper flat numbers which are primes arise in the study of multi-perfect numbers. Here we show that the lower or upper flat primes have asymptotic density relative to that of the full set of primes given by twice Artin’s constant, that more than 53% of the primes are both lower and upper flat, and that the series of reciprocals of the lower or the upper thin primes converges.
Cambridge University Press
This article was published in the Bulletin of the Australian Mathematical Society. Copyright 2010 Australian Mathematical Publishing Association Inc.