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Meissel's mathematical work covers a number of areas. He worked on prime numbers giving the result that there are 50847478 primes less than 10
. Lehmer showed, 70 years later, that this is 56 too few. In addition to other number theory work on Möbius inversion and the theory of partitions, Meissel wrote on Bessel functions, asymptotic analysis, refraction of light and the three body problem.
His main skill was in numerical calculations and manipulation of complicated expressions. His work was based on the mathematics he learnt as a student and he appears not to have kept up with new developments.
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