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PSLQ and Hex Digits of Pi

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PSLQ and Hex Digits of Pi. Finalist for the $100K Edge of Computation Prize. My brother made the observation that this log formula allows one to compute binary digits of log 2 without knowing the previous ones! ( a BBP formula ). - PowerPoint PPT Presentation

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PSLQ and Hex Digits of Pi My brother made the observation that this log formula allows one to compute binary digits of log 2 without knowing the previous ones! (a BBP formula) This reduced to which Maple, Mathematica and humans can easily prove. A triumph for “reverse engineered mathematics” [algorithm design] Bailey, Plouffe and he hunted for such a formula for Pi. Three months later the computer - doing bootstrapped PSLQ hunts - returned: No such formula exists base-ten (provably) Finalist for the $100K Edge of Computation Prize

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Page 1: PSLQ and Hex Digits of Pi

PSLQ and Hex Digits of Pi

My brother made the observation that this log formulaallows one to compute binary digits of log 2 without

knowing the previous ones! (a BBP formula)

This reduced to

which Maple, Mathematica and humans can easily prove.

A triumph for “reverse engineered mathematics” [algorithm design]

Bailey, Plouffe and he hunted for such a formula for Pi. Three months later the computer - doing bootstrapped PSLQ hunts - returned:

No such formula exists base-ten (provably)

Finalist for the $100K Edge of Computation Prize

Page 2: PSLQ and Hex Digits of Pi

PSLQ and Hex Digits of Pi

No such formula exists base-ten (provably)

Finalist for the $100K Edge of Computation Prize

won by David Deutsch

Page 3: PSLQ and Hex Digits of Pi

J Borwein Abacus User and Computer Racer

P Borwein Grid User

D Borwein Slide Rule User

The pre-designed Algorithm ran the next day

T Borwein Gamer

Now built into some compilers!

Used to check trillion digit hex-computation of Pi

JJ Borwein Skyper

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