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Approximations to the Distribution of Primes
The function
, the prime-counting function, gives the number of primes less than or equal to
. The plots shown are of the differences between
and the approximations to
due to Gauss, Legendre, and Riemann.
Contributed by:
Enrique Zeleny
THINGS TO TRY
Automatic Animation
SNAPSHOTS
DETAILS
These are the approximations:
Gauss (integral logarithm)
,
Legendre
,
and Riemann
.
RELATED LINKS
Prime Number Theorem
(
Wolfram
MathWorld
)
Prime Counting Function
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Approximations to the Distribution of Primes
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ApproximationsToTheDistributionOfPrimes/
Contributed by:
Enrique Zeleny
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