Reversible primes
C\'ecile Dartyge, Bruno Martin, Jo\"el Rivat, Igor E. Shparlinski,, Cathy Swaenepoel

TL;DR
This paper investigates properties of n-bit integers and their digit reversals, providing bounds on primes, prime factors, and squarefree numbers, along with exponential sum estimates related to these reversals.
Contribution
It introduces new bounds and asymptotic formulas for primes, prime factors, and squarefree integers with digit reversal properties, using sieve and exponential sum techniques.
Findings
Upper bound on expected primes where p and reversed p are prime
Lower bound on integers with bounded prime factors and their reversals
Asymptotic count of n-bit integers with both number and reversal being squarefree
Abstract
For an -bit positive integer written in binary as where, , , , let us define the digital reversal of . Also let With a sieve argument, we obtain an upper bound of the expected order of magnitude for the number of such that and are prime. We also prove that for sufficiently large , where denotes the number of prime factors counted with multiplicity of and is an absolute constant. Finally, we provide an asymptotic formula for the…
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Analytic Number Theory Research · Coding theory and cryptography
