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SUMMARY:Carl Pomerance (Dartmouth College)
DTSTART:20200603T170000Z
DTEND:20200603T172500Z
DTSTAMP:20260423T011321Z
UID:CANT2020/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/35/
 ">Symmetric primes</a>\nby Carl Pomerance (Dartmouth College) as part of C
 ombinatorial and additive number theory (CANT 2021)\n\n\nAbstract\nTwo odd
  primes $p\,q$ are said to form a symmetric pair if\n$|p-q|=\\gcd(p-1\,q-1
 )$\, and we say a prime is symmetric if it belongs\nto some symmetric pair
 .  The concept comes from a standard proof\nof quadratic reciprocity where
  one counts lattice points in the\n$p/2\\times q/2$ rectangle nestled in t
 he first quadrant\, both above\nand below the diagonal:  $p$ and $q$ are a
  symmetric pair if and only if\nthese counts agree.  Over 20 years ago\, F
 letcher\, Lindgren\, and I\nshowed that most primes are {\\it not} symmetr
 ic\, though the numerical \nevidence for this is very weak\n(only about $1
 /6$ of the primes to $10^6$ are asymmetric).  In a\nnew paper with Banks a
 nd Pollack we get a conjecturally tight\nupper bound for the distribution 
 of symmetric primes and we prove\nthat there are infinitely many of them.\
 n
LOCATION:https://researchseminars.org/talk/CANT2020/35/
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