Actually the history of calculations of pi(x) is rife with problems. Aside from Meissel's mistaken value of pi(10^9) (not Bertelsen), which was caught by D. H. Lehmer and his students when they implemented a version of Meissel's method on the SWAC computer, Lehmer's group, themselves, had an erroneous value for pi(10^11) (off by 1, which Lehmer later attributed to a hardware error on a tape drive). The next one on the list was Jan Bohman, who implemented Mapes' (a Ph.D. student of Lehmer's) method on a Univac 1108. He calculated a bunch of values of pi(x), with the largest x being 10^13. When I started on the algorithm described in the paper by me, Lagarias and Odlyzko, I verified all of the earlier values, except for Bohman's value of pi(10^13) which was off by 949. I spent a few days looking for a non-existent bug -- I was right and he was wrong. A few people suggested to me that I avoid the curse by not publishing the largest value that I computed, but I thought that that was wimpling out. I included various consistency checks, which did the trick. Victor On Wed, Aug 30, 2017 at 2:16 AM, James Cloos <cloos@jhcloos.com> wrote:
"TR" == Tomas Rokicki <rokicki@gmail.com> writes:
TR> Bertelsen's Number. I story I had not heard before. Do a google search TR> and you'll see that value pop up in a bunch of recent places.
I love mathworld's explanation:
Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478.ยน
I cannot right now recall another such trio of erroneous. :)
1] from http://mathworld.wolfram.com/BertelsensNumber.html
-JimC -- James Cloos <cloos@jhcloos.com> OpenPGP: 0x997A9F17ED7DAEA6
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