Experimental Mathematics

Prime Numbers with a Fixed Number of One Bits or Zero Bits in Their Binary Representation

Samuel S. Wagstaff, Jr.

Abstract

We study the distribution of prime numbers that have a given number of one bits in their binary representation, and of those that have a given number of zero bits. We consider basic questions such as whether there are infinitely many of them, and explain their distribution in residue classes modulo small primes. We prove the unexpected result that, for m ≥ 3, there is no prime number with precisely 2m bits, exactly two of which are zero bits.

Article information

Source
Experiment. Math., Volume 10, Issue 2 (2001), 267-274.

Dates
First available in Project Euclid: 30 August 2001

Permanent link to this document
https://projecteuclid.org/euclid.em/999188636

Mathematical Reviews number (MathSciNet)
MR1837675

Zentralblatt MATH identifier
1046.11089

Keywords
prime numbers binary representation

Citation

Wagstaff, Samuel S. Prime Numbers with a Fixed Number of One Bits or Zero Bits in Their Binary Representation. Experiment. Math. 10 (2001), no. 2, 267--274. https://projecteuclid.org/euclid.em/999188636


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