Il existe 4 périodes de 13 chiffres pour n/53 en base 10.

Pour toutes les fractions de n/53 en base 10, la période de 1/53 revient alors 13 fois (en orange)

1/53=0,0188679245283...

2/53=0,0377358490566...

3/53=0,0566037735849...

4/53=0,0754716981132...

5/53=0,0943396226415...

6/53=0,1132075471698...

7/53=0,1320754716981...

8/53=0,1509433962264...

9/53=0,1698113207547...

10/53=0,1886792452830...

11/53=0,2075471698113...

12/53=0,2264150943396...

13/53=0,2452830188679...

14/53=0,2641509433962...

15/53=0,2830188679245...

16/53=0,3018867924528...

17/53=0,3207547169811...

18/53=0,3396226415094...

19/53=0,3584905660377...

20/53=0,3773584905660...

21/53=0,3962264150943...

22/53=0,4150943396226...

23/53=0,4339622641509...

24/53=0,4528301886792...

25/53=0,4716981132075...

26/53=0,4905660377358...

27/53=0,5094339622641...

28/53=0,5283018867924...

29/53=0,5471698113207...

30/53=0,5660377358490...

31/53=0,5849056603773...

32/53=0,6037735849056...

33/53=0,6226415094339...

34/53=0,6415094339622...

35/53=0,6603773584905...

36/53=0,6792452830188...

37/53=0,6981132075471...

38/53=0,7169811320754...

39/53=0,7358490566037...

40/53=0,7547169811320...

41/53=0,7735849056603...

42/53=0,7924528301886...

43/53=0,8113207547169...

44/53=0,8301886792452...

45/53=0,8490566037735...

46/53=0,8679245283018...

47/53=0,8867924528301...

48/53=0,9056603773584...

49/53=0,9245283018867...

50/53=0,9433962264150...

51/53=0,9622641509433...

52/53=0,9811320754716...

On remarque que le produit du nombre de périodes (4) et de leurs longueurs (13) est égal à 52 et donc au premier -1.