Il existe 2 périodes de 29 chiffres pour n/59 en base 5.

Pour toutes les fractions de n/59 en base 5, la période de 1/59 revient alors 29 fois (en orange)

1/59=0,00202440340132141301113422121...

2/59=0,00410431230314333102232344242...

3/59=0,01113422121002024403401321413...

4/59=0,01321413011134221210020244034...

5/59=0,02024403401321413011134221210...

6/59=0,02232344242004104312303143331...

7/59=0,02440340132141301113422121002...

8/59=0,03143331022323442420041043123...

9/59=0,03401321413011134221210020244...

10/59=0,04104312303143331022323442420...

11/59=0,04312303143331022323442420041...

12/59=0,10020244034013214130111342212...

13/59=0,10223234424200410431230314333...

14/59=0,10431230314333102232344242004...

15/59=0,11134221210020244034013214130...

16/59=0,11342212100202440340132141301...

17/59=0,12100202440340132141301113422...

18/59=0,12303143331022323442420041043...

19/59=0,13011134221210020244034013214...

20/59=0,13214130111342212100202440340...

21/59=0,13422121002024403401321413011...

22/59=0,14130111342212100202440340132...

23/59=0,14333102232344242004104312303...

24/59=0,20041043123031433310223234424...

25/59=0,20244034013214130111342212100...

26/59=0,21002024403401321413011134221...

27/59=0,21210020244034013214130111342...

28/59=0,21413011134221210020244034013...

29/59=0,22121002024403401321413011134...

30/59=0,22323442420041043123031433310...

31/59=0,23031433310223234424200410431...

32/59=0,23234424200410431230314333102...

33/59=0,23442420041043123031433310223...

34/59=0,24200410431230314333102232344...

35/59=0,24403401321413011134221210020...

36/59=0,30111342212100202440340132141...

37/59=0,30314333102232344242004104312...

38/59=0,31022323442420041043123031433...

39/59=0,31230314333102232344242004104...

40/59=0,31433310223234424200410431230...

41/59=0,32141301113422121002024403401...

42/59=0,32344242004104312303143331022...

43/59=0,33102232344242004104312303143...

44/59=0,33310223234424200410431230314...

45/59=0,34013214130111342212100202440...

46/59=0,34221210020244034013214130111...

47/59=0,34424200410431230314333102232...

48/59=0,40132141301113422121002024403...

49/59=0,40340132141301113422121002024...

50/59=0,41043123031433310223234424200...

51/59=0,41301113422121002024403401321...

52/59=0,42004104312303143331022323442...

53/59=0,42212100202440340132141301113...

54/59=0,42420041043123031433310223234...

55/59=0,43123031433310223234424200410...

56/59=0,43331022323442420041043123031...

57/59=0,44034013214130111342212100202...

58/59=0,44242004104312303143331022323...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (29) est égal à 58 et donc au premier -1.