Il existe 2 périodes de 35 chiffres pour n/71 en base 2.

Pour toutes les fractions de n/71 en base 2, la période de 1/71 revient alors 35 fois (en orange)

1/71=0,00000011100110110000101011010001001...

2/71=0,00000111001101100001010110100010010...

3/71=0,00001010110100010010000001110011011...

4/71=0,00001110011011000010101101000100100...

5/71=0,00010010000001110011011000010101101...

6/71=0,00010101101000100100000011100110110...

7/71=0,00011001001111010100101110110111111...

8/71=0,00011100110110000101011010001001000...

9/71=0,00100000011100110110000101011010001...

10/71=0,00100100000011100110110000101011010...

11/71=0,00100111101010010111011011111100011...

12/71=0,00101011010001001000000111001101100...

13/71=0,00101110110111111000110010011110101...

14/71=0,00110010011110101001011101101111110...

15/71=0,00110110000101011010001001000000111...

16/71=0,00111001101100001010110100010010000...

17/71=0,00111101010010111011011111100011001...

18/71=0,01000000111001101100001010110100010...

19/71=0,01000100100000011100110110000101011...

20/71=0,01001000000111001101100001010110100...

21/71=0,01001011101101111110001100100111101...

22/71=0,01001111010100101110110111111000110...

23/71=0,01010010111011011111100011001001111...

24/71=0,01010110100010010000001110011011000...

25/71=0,01011010001001000000111001101100001...

26/71=0,01011101101111110001100100111101010...

27/71=0,01100001010110100010010000001110011...

28/71=0,01100100111101010010111011011111100...

29/71=0,01101000100100000011100110110000101...

30/71=0,01101100001010110100010010000001110...

31/71=0,01101111110001100100111101010010111...

32/71=0,01110011011000010101101000100100000...

33/71=0,01110110111111000110010011110101001...

34/71=0,01111010100101110110111111000110010...

35/71=0,01111110001100100111101010010111011...

36/71=0,10000001110011011000010101101000100...

37/71=0,10000101011010001001000000111001101...

38/71=0,10001001000000111001101100001010110...

39/71=0,10001100100111101010010111011011111...

40/71=0,10010000001110011011000010101101000...

41/71=0,10010011110101001011101101111110001...

42/71=0,10010111011011111100011001001111010...

43/71=0,10011011000010101101000100100000011...

44/71=0,10011110101001011101101111110001100...

45/71=0,10100010010000001110011011000010101...

46/71=0,10100101110110111111000110010011110...

47/71=0,10101001011101101111110001100100111...

48/71=0,10101101000100100000011100110110000...

49/71=0,10110000101011010001001000000111001...

50/71=0,10110100010010000001110011011000010...

51/71=0,10110111111000110010011110101001011...

52/71=0,10111011011111100011001001111010100...

53/71=0,10111111000110010011110101001011101...

54/71=0,11000010101101000100100000011100110...

55/71=0,11000110010011110101001011101101111...

56/71=0,11001001111010100101110110111111000...

57/71=0,11001101100001010110100010010000001...

58/71=0,11010001001000000111001101100001010...

59/71=0,11010100101110110111111000110010011...

60/71=0,11011000010101101000100100000011100...

61/71=0,11011011111100011001001111010100101...

62/71=0,11011111100011001001111010100101110...

63/71=0,11100011001001111010100101110110111...

64/71=0,11100110110000101011010001001000000...

65/71=0,11101010010111011011111100011001001...

66/71=0,11101101111110001100100111101010010...

67/71=0,11110001100100111101010010111011011...

68/71=0,11110101001011101101111110001100100...

69/71=0,11111000110010011110101001011101101...

70/71=0,11111100011001001111010100101110110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (35) est égal à 70 et donc au premier -1.