
Glossary: Prime Pages: Top 5000: 
We define p# (pprimorial) to be the
product of the primes less than or equal to p. For
example:
It is customary to only apply the notation p# to primes p, but some authors will apply it to any positive real number (e.g., 10.72# = 2^{.}3^{.}5^{.}7 = 210). When viewed this way, the function log(x#) is Tschebycheff's function, and the prime number theorem is equivalent to the expression log x# ~ x,(i.e., (log x#)/x approaches 1 as x approaches infinity.)
See Also: Factorial, FactorialPrime, MultifactorialPrime Related pages (outside of this work) Chris K. Caldwell © 19992017 (all rights reserved)
