| Wilson's Theorem |
| 0 |
1 |
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3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
| 1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 2 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 3 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 4 |
1 |
2 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 5 |
1 |
2 |
1 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 6 |
1 |
2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 7 |
1 |
2 |
6 |
3 |
1 |
6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 8 |
1 |
2 |
6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 9 |
1 |
2 |
6 |
6 |
3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 10 |
1 |
2 |
6 |
4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 11 |
1 |
2 |
6 |
2 |
10 |
5 |
2 |
5 |
1 |
10 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 12 |
1 |
2 |
6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 13 |
1 |
2 |
6 |
11 |
3 |
5 |
9 |
7 |
11 |
6 |
1 |
12 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 14 |
1 |
2 |
6 |
10 |
8 |
6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 15 |
1 |
2 |
6 |
9 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 16 |
1 |
2 |
6 |
8 |
8 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 17 |
1 |
2 |
6 |
7 |
1 |
6 |
8 |
13 |
15 |
14 |
1 |
12 |
3 |
8 |
1 |
16 |
0 |
0 |
0 |
0 |
| 18 |
1 |
2 |
6 |
6 |
12 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 19 |
1 |
2 |
6 |
5 |
6 |
17 |
5 |
2 |
18 |
9 |
4 |
10 |
16 |
15 |
16 |
9 |
1 |
18 |
0 |
0 |
If p is prime, then (p-1)! + 1 is divisible by p.