# Definition:Euclid Number/Sequence

 $\displaystyle E_0 \ \$ $\displaystyle = p_0\# + 1$ $=$ $\displaystyle 1 + 1$ $\displaystyle = 2$ $\displaystyle E_1 \ \$ $\displaystyle = p_1\# + 1$ $=$ $\displaystyle 2 + 1$ $\displaystyle = 3$ $\displaystyle E_2 \ \$ $\displaystyle = p_2\# + 1$ $=$ $\displaystyle 2 \times 3 + 1$ $\displaystyle = 7$ $\displaystyle E_3 \ \$ $\displaystyle = p_3\# + 1$ $=$ $\displaystyle 2 \times 3 \times 5 + 1$ $\displaystyle = 31$ $\displaystyle E_4 \ \$ $\displaystyle = p_4\# + 1$ $=$ $\displaystyle 2 \times 3 \times 5 \times 7 + 1$ $\displaystyle = 211$ $\displaystyle E_5 \ \$ $\displaystyle = p_5\# + 1$ $=$ $\displaystyle 2 \times 3 \times 5 \times 7 \times 11 + 1$ $\displaystyle = 2311$ $\displaystyle E_6 \ \$ $\displaystyle = p_6\# + 1$ $=$ $\displaystyle 2 \times 3 \times 5 \times 7 \times 11 \times 13 + 1$ $\displaystyle = 30031$