\begin{definition}[Definition:Euclid Number/Sequence]
The sequence of Euclid numbers begins as follows:
{{begin-eqn}}
{{eqn | ll= E_0
      | l = = p_0\# + 1
      | r = 1 + 1
      | rr= = 2
      | c = 
}}
{{eqn | ll= E_1
      | l = = p_1\# + 1
      | r = 2 + 1
      | rr= = 3
      | c = 
}}
{{eqn | ll= E_2
      | l = = p_2\# + 1
      | r = 2 \times 3 + 1
      | rr= = 7
      | c = 
}}
{{eqn | ll= E_3
      | l = = p_3\# + 1
      | r = 2 \times 3 \times 5 + 1
      | rr= = 31
      | c = 
}}
{{eqn | ll= E_4
      | l = = p_4\# + 1
      | r = 2 \times 3 \times 5 \times 7 + 1
      | rr= = 211
      | c = 
}}
{{eqn | ll= E_5
      | l = = p_5\# + 1
      | r = 2 \times 3 \times 5 \times 7 \times 11 + 1
      | rr= = 2311
      | c = 
}}
{{eqn | ll= E_6
      | l = = p_6\# + 1
      | r = 2 \times 3 \times 5 \times 7 \times 11 \times 13 + 1
      | rr= = 30031
      | c = 
}}
{{end-eqn}}
{{OEIS|A006862}}
Category:Definitions/Euclid Numbers
\end{definition}