  Prime numbers have attracted the attention of mathematiciansand enthusiasts
for millenniums due to their simple definition and remarkable properties. In
this paper, we study primorial numbers (the product of the first prime numbers)
to define primorial sets, primorial intervals, primorial tables, and primorial
totative numbers. We establish relationships between prime numbers and
primorial totative numbers and between admissible k-tuples of prime numbers and
admissible k-tuples of primorial totative. Finally, we study the Goldbach
conjecture and derive four Goldbach conjectures using primordial intervals,
twin, cousin, and sexy prime numbers.
