Definition:Primorial/Examples

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Examples of Primorials

The first few primorials (of both types) are as follows:

\(\displaystyle 0\# \ \ \) \(\displaystyle = p_0 \#\) \(=\) \(\displaystyle \) \(\displaystyle = 1\)
\(\displaystyle 1\# \ \ \) \(\displaystyle = p_0 \#\) \(=\) \(\displaystyle \) \(\displaystyle = 1\)
\(\displaystyle 2\# \ \ \) \(\displaystyle = p_1 \#\) \(=\) \(\displaystyle \) \(\displaystyle = 2\)
\(\displaystyle 3\# \ \ \) \(\displaystyle = p_2\#\) \(=\) \(\displaystyle 2 \times 3\) \(\displaystyle = 6\)
\(\displaystyle 4\# \ \ \) \(\displaystyle = p_2\#\) \(=\) \(\displaystyle 2 \times 3\) \(\displaystyle = 6\)
\(\displaystyle 5\# \ \ \) \(\displaystyle = p_3\#\) \(=\) \(\displaystyle 2 \times 3 \times 5\) \(\displaystyle = 30\)
\(\displaystyle 6\# \ \ \) \(\displaystyle = p_3\#\) \(=\) \(\displaystyle 2 \times 3 \times 5\) \(\displaystyle = 30\)
\(\displaystyle 7\# \ \ \) \(\displaystyle = p_4\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7\) \(\displaystyle = 210\)
\(\displaystyle 8\# \ \ \) \(\displaystyle = p_4\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7\) \(\displaystyle = 210\)
\(\displaystyle 9\# \ \ \) \(\displaystyle = p_4\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7\) \(\displaystyle = 210\)
\(\displaystyle 10\# \ \ \) \(\displaystyle = p_4\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7\) \(\displaystyle = 210\)
\(\displaystyle 11\# \ \ \) \(\displaystyle = p_5\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7 \times 11\) \(\displaystyle = 2310\)
\(\displaystyle 12\# \ \ \) \(\displaystyle = p_5\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7 \times 11\) \(\displaystyle = 2310\)
\(\displaystyle 13\# \ \ \) \(\displaystyle = p_6\#\) \(=\) \(\displaystyle 2 \times 3 \times 5 \times 7 \times 11 \times 13\) \(\displaystyle = 30 \, 030\)

The sequence contines:

$1, 2, 6, 30, 210, 2310, 30 \, 030, 510 \, 510, 9 \, 699 \, 690, 223 \, 092 \, 870, \ldots$

This sequence is A002110 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Sources