Dozenal Wiki
Advertisement

08579214E36429X7 is the cyclic number generated from the prime 15. It is the third-smallest cyclic number, the two smaller ones being 2497 (from 5) and 186X35 (from 7). E and 11 do not generate cyclic numbers. The number 08579214E36429X7 contains all the digits at least once, and 2, 4, 9, and 7 repeat.

Primes that generate cyclic numbers: 5, 7, 15, 27, 35, 37, 45, 57, 85, 87, 95, X7, E5, E7...

The next 2 cyclic numbers are from 27 and 35 and are: 0478XX093598166E74311E28623X55 and 036190X653277397X9E4E85X2E15689448241207.

Calculation[]

1 × 08579214E36429X7 = 08579214E36429X7
2 × 08579214E36429X7 = 14E36429X7085792
3 × 08579214E36429X7 = 214E26429X705879
4 × 08579214E36429X7 = 29X708579214E364
5 × 08579214E36429X7 = 36429X708579214E
6 × 08579214E36429X7 = 429X708579214E36
7 × 08579214E36429X7 = 4E36429X70857921
8 x 08579214E36429X7 = 579214E36429X708
9 x 08579214E36429X7 = 6429X708579214E3
X x 08579214E36429X7 = 708579214E36429X
E x 08579214E36429X7 = 79214E36429X7085
10 x 08579214E36429X7 = 8579214E36429X70
11 x 08579214E36429X7 = 9214E36429X70857
12 x 08579214E36429X7 = 9X708579214E3642
13 x 08579214E36429X7 = X708579214E36429
14 x 08579214E36429X7 = E36428X708579214
15 x 08579214E36429X7 = EEEEEEEEEEEEEEEE

If multiplying by an integer greater than 15, there is a simple process to get to a cyclic permutation of 08579214E36429X7. By adding the rightmost dozen-four digits to the remaining digits and repeating this process until only dozen-four digits are left, it will result in a cyclic permutation of 08579214E36429X7:

08579214E36429X7 × 16 = 108579214E36429X6
1 + 08579214E36429X6 = 08579214E36429X7
08579214E36429X7 × 30 = 214E26429X7058790
2 + 14E26429X7058790 = 14E36429X7085792

Multiplying by a multiple of 15 will result in EEEEEEEEEEEEEEEE through this process:

08579214E36429X7 × 2X = 2EEEEEEEEEEEEEEEE9
2 + EEEEEEEEEEEEEEEE9 = EEEEEEEEEEEEEEEE
Advertisement