A number which is the product of the first n composite numbers. more
The compositorials up to 10
15 :
1,
4,
24,
192,
1728,
17280,
207360,
2903040,
43545600,
696729600,
12541132800,
250822656000,
5267275776000,
115880067072000.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 10000 values, from 1 to 6.9⋅1036312).
n\r | 0 | 1 |
2 | 9999 | 1 | 2 |
3 | 9998 | 2 | 0 | 3 |
4 | 9999 | 1 | 0 | 0 | 4 |
5 | 9995 | 1 | 1 | 1 | 2 | 5 |
6 | 9998 | 1 | 0 | 0 | 1 | 0 | 6 |
7 | 9993 | 1 | 0 | 2 | 2 | 0 | 2 | 7 |
8 | 9998 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 8 |
9 | 9996 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 9 |
10 | 9995 | 1 | 1 | 0 | 2 | 0 | 0 | 0 | 1 | 0 | 10 |
11 | 9987 | 2 | 1 | 0 | 2 | 1 | 1 | 1 | 1 | 1 | 3 |
A pictorial representation of the table above
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.