10054
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Extending Rosser's Theorem
Let
be the number of primes up to
. The prime number theorem states that
and implies that
, where
is the
prime. Rosser proved that
for all
. Rosser's theorem was extended to
, for all
.
The curves plotted are
(blue),
(khaki), and
(brown).
Contributed by:
Jon Perry
THINGS TO TRY
Slider Zoom
Automatic Animation
SNAPSHOTS
RELATED LINKS
Rosser's Theorem
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Extending Rosser's Theorem
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/ExtendingRossersTheorem/
Contributed by:
Jon Perry
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Dirichlet's Theorem
Jay Warendorff
Fermat's Little Theorem
Michael Schreiber
Fundamental Theorem of Arithmetic
Hector Zenil
Wilson's Theorem in Disguise
Oleksandr Pavlyk and Brett Champion
The Prime Number Theorem
Stephen Wolfram
Fermat's 4n+1 Theorem and the n Queens Problem
Jay Warendorff
An Approximation to the n-th Prime Number
Jon Perry
Coloring Cycle Decompositions in Complete Graphs on a Prime Number of Vertices
Michael Morrison
Factoring Time
Jesse Friedman
Correlating the Mertens Function with the Farey Sequence
Jenda Vondra
Related Topics
Number Theory
Prime Numbers
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+