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SUMMARY:Cathy Swaenepoel (Université Paris Cité)
DTSTART:20240130T130000Z
DTEND:20240130T140000Z
DTSTAMP:20260423T021336Z
UID:OWNS/125
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWNS/125/">R
 eversible primes</a>\nby Cathy Swaenepoel (Université Paris Cité) as par
 t of One World Numeration seminar\n\n\nAbstract\nThe properties of the dig
 its of prime numbers and various other\nsequences of integers have attract
 ed great interest in recent years.\nFor any positive integer $k$\, we deno
 te by $\\overleftarrow{k}$ the\nreverse of $k$ in base 2\, defined by $\\o
 verleftarrow{k} = \\sum_{j=0}^{n-1} \\varepsilon_j\\\,2^{n-1-j}$ where $k 
 = \\sum_{j=0}^{n-1} \\varepsilon_{j} \\\,2^j$ with $\\varepsilon_j \\in \\
 {0\,1\\}$\, $j\\in\\{0\, \\ldots\, n-1\\}$\, $ \\varepsilon_{n-1} = 1$. A 
 natural question is to estimate the number\nof primes $p\\in \\left[2^{n-1
 }\,2^n\\right)$ such that\n$\\overleftarrow{p}$ is prime.  We will present
  a result which provides\nan upper bound of the expected order of magnitud
 e. Our method is based\non a sieve argument and also allows us to obtain a
  strong lower bound\nfor the number of integers $k$ such that $k$ and $\\o
 verleftarrow{k}$\nhave at most 8 prime factors (counted with multiplicity)
 . We will also\npresent an asymptotic formula for the number of integers\n
 $k\\in \\left[2^{n-1}\,2^n\\right)$ such that $k$ and $\\overleftarrow{k}$
 \nare squarefree.\n\nThis is a joint work with Cécile Dartyge\, Bruno Mar
 tin\,\nJoël Rivat and Igor Shparlinski.\n
LOCATION:https://researchseminars.org/talk/OWNS/125/
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