Hi,
Ramanujan supposedly discovered that the number, 163, has this interesting
property that exp(sqrt(163)*pi), which is obviously a transcendental number, is
real close to an integer (close to 10^(-12)).
If I compute this using the Wolfram alpha engine, I get:
262537412640768743.99999999999925007259719818568887935385...
When I do this in R 3.1.1 (64-bit windows), I get:
262537412640768256.0000
The absolute error between the exact and R's value is 488, with a relative
error of about 1.9x10^(-15).
In order to replicate Wolfram Alpha, I tried doing this in "Rmfpr" but I am
unable to get accurate results:
library(Rmpfr)
> exp(sqrt(163) * mpfr(pi, 120))
1 'mpfr' number of precision 120 bits
[1] 262537412640767837.08771354274620169031
The above answer is not only inaccurate, but it is actually worse than the
answer using the usual double precision. Any thoughts as to what I am doing
wrong?
Thank you,
Ravi
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