Il existe 6 périodes de 13 chiffres pour n/79 en base 10.

Pour toutes les fractions de n/79 en base 10, la période de 1/79 revient alors 13 fois (en orange)

1/79=0,0126582278481...

2/79=0,0253164556962...

3/79=0,0379746835443...

4/79=0,0506329113924...

5/79=0,0632911392405...

6/79=0,0759493670886...

7/79=0,0886075949367...

8/79=0,1012658227848...

9/79=0,1139240506329...

10/79=0,1265822784810...

11/79=0,1392405063291...

12/79=0,1518987341772...

13/79=0,1645569620253...

14/79=0,1772151898734...

15/79=0,1898734177215...

16/79=0,2025316455696...

17/79=0,2151898734177...

18/79=0,2278481012658...

19/79=0,2405063291139...

20/79=0,2531645569620...

21/79=0,2658227848101...

22/79=0,2784810126582...

23/79=0,2911392405063...

24/79=0,3037974683544...

25/79=0,3164556962025...

26/79=0,3291139240506...

27/79=0,3417721518987...

28/79=0,3544303797468...

29/79=0,3670886075949...

30/79=0,3797468354430...

31/79=0,3924050632911...

32/79=0,4050632911392...

33/79=0,4177215189873...

34/79=0,4303797468354...

35/79=0,4430379746835...

36/79=0,4556962025316...

37/79=0,4683544303797...

38/79=0,4810126582278...

39/79=0,4936708860759...

40/79=0,5063291139240...

41/79=0,5189873417721...

42/79=0,5316455696202...

43/79=0,5443037974683...

44/79=0,5569620253164...

45/79=0,5696202531645...

46/79=0,5822784810126...

47/79=0,5949367088607...

48/79=0,6075949367088...

49/79=0,6202531645569...

50/79=0,6329113924050...

51/79=0,6455696202531...

52/79=0,6582278481012...

53/79=0,6708860759493...

54/79=0,6835443037974...

55/79=0,6962025316455...

56/79=0,7088607594936...

57/79=0,7215189873417...

58/79=0,7341772151898...

59/79=0,7468354430379...

60/79=0,7594936708860...

61/79=0,7721518987341...

62/79=0,7848101265822...

63/79=0,7974683544303...

64/79=0,8101265822784...

65/79=0,8227848101265...

66/79=0,8354430379746...

67/79=0,8481012658227...

68/79=0,8607594936708...

69/79=0,8734177215189...

70/79=0,8860759493670...

71/79=0,8987341772151...

72/79=0,9113924050632...

73/79=0,9240506329113...

74/79=0,9367088607594...

75/79=0,9493670886075...

76/79=0,9620253164556...

77/79=0,9746835443037...

78/79=0,9873417721518...

On remarque que le produit du nombre de périodes (6) et de leurs longueurs (13) est égal à 78 et donc au premier -1.