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Bernstein's constant doesn't strictly fit the parameters of the question, but it's notable as a more recent "Legendre-type" example. Bernstein conjectured that his constant was exactly $\frac{1}{2\sqrt{\pi}}$ in 1914; it wasn't until the '80s that it became possible to compute enough digits to refu(dia)te the conjecture. Although perhaps it wasn't surprising -- I have no idea whether Bernstein's conjecture was generally believed; can anyone shed light on that? |
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Post Made Community Wiki by S. Carnahan♦
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Bernstein's constant doesn't strictly fit the parameters of the question, but it's notable as a more recent "Legendre-type" example. Bernstein conjectured that his constant was exactly $\frac{1}{2\sqrt{\pi}}$ in 1914; it wasn't until the '80s that it became possible to compute enough digits to refu(dia)te the conjecture. Although perhaps it wasn't surprising -- I have no idea whether Bernstein's conjecture was generally believed; can anyone shed light on that? |
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