Bertelsen's number is an erroneous name erroneously given to the erroneous value of ,
where
is the prime counting function. This value
is 56 lower than the correct value of . Ore (1988, p. 69) states that the erroneous value
478 originated in Bertelsen's application
of Meissel's method in 1893 (MathPages; Prime Curios!). However, the incorrect value
actually first appears in Meissel (1885) rather than Bertelsen in 1893, as correctly
noted by Lagarias et al. 1985. (Note that MathPages incorrectly states that
Lagarias et al. attribute the result to Bertelsen.)
Unfortunately, the incorrect value has continued to be propagated in modern works such as Hardy and Wright (1979, p. 9), Davis and Hersch (1981, p. 175;
but actually given correctly in the table on p. 213), Sondheimer (1981), Kramer
(1983), Ore (1988, p. 77), and Cormen et al. (1990).