Il existe 2 périodes de 23 chiffres pour n/47 en base 2.

Pour toutes les fractions de n/47 en base 2, la période de 1/47 revient alors 23 fois (en orange)

1/47=0,00000101011100100110001...

2/47=0,00001010111001001100010...

3/47=0,00010000010101110010011...

4/47=0,00010101110010011000100...

5/47=0,00011011001110111110101...

6/47=0,00100000101011100100110...

7/47=0,00100110001000001010111...

8/47=0,00101011100100110001000...

9/47=0,00110001000001010111001...

10/47=0,00110110011101111101010...

11/47=0,00111011111010100011011...

12/47=0,01000001010111001001100...

13/47=0,01000110110011101111101...

14/47=0,01001100010000010101110...

15/47=0,01010001101100111011111...

16/47=0,01010111001001100010000...

17/47=0,01011100100110001000001...

18/47=0,01100010000010101110010...

19/47=0,01100111011111010100011...

20/47=0,01101100111011111010100...

21/47=0,01110010011000100000101...

22/47=0,01110111110101000110110...

23/47=0,01111101010001101100111...

24/47=0,10000010101110010011000...

25/47=0,10001000001010111001001...

26/47=0,10001101100111011111010...

27/47=0,10010011000100000101011...

28/47=0,10011000100000101011100...

29/47=0,10011101111101010001101...

30/47=0,10100011011001110111110...

31/47=0,10101000110110011101111...

32/47=0,10101110010011000100000...

33/47=0,10110011101111101010001...

34/47=0,10111001001100010000010...

35/47=0,10111110101000110110011...

36/47=0,11000100000101011100100...

37/47=0,11001001100010000010101...

38/47=0,11001110111110101000110...

39/47=0,11010100011011001110111...

40/47=0,11011001110111110101000...

41/47=0,11011111010100011011001...

42/47=0,11100100110001000001010...

43/47=0,11101010001101100111011...

44/47=0,11101111101010001101100...

45/47=0,11110101000110110011101...

46/47=0,11111010100011011001110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (23) est égal à 46 et donc au premier -1.