primorialWe define p# (p-primorial) to be the product of the primes less than or equal to p. For example:
- 3# = 2.3 = 6,
- 5# = 2.3.5 = 30, and
- 13# = 18.104.22.168.11.13 = 30030.
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# = 22.214.171.124 = 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.)
Related pages (outside of this work)