Il existe 2 périodes de 95 chiffres pour n/191 en base 2.

Pour toutes les fractions de n/191 en base 2, la période de 1/191 revient alors 95 fois (en orange)

1/191=0,00000001010101110001111011010011110001010000011010110011100110100010001011011001001000011000001...

2/191=0,00000010101011100011110110100111100010100000110101100111001101000100010110110010010000110000010...

3/191=0,00000100000001010101110001111011010011110001010000011010110011100110100010001011011001001000011...

4/191=0,00000101010111000111101101001111000101000001101011001110011010001000101101100100100001100000100...

5/191=0,00000110101100111001101000100010110110010010000110000010000000101010111000111101101001111000101...

6/191=0,00001000000010101011100011110110100111100010100000110101100111001101000100010110110010010000110...

7/191=0,00001001011000011101011111001010011000110010111011101001001101101111001111101111111010101000111...

8/191=0,00001010101110001111011010011110001010000011010110011100110100010001011011001001000011000001000...

9/191=0,00001100000100000001010101110001111011010011110001010000011010110011100110100010001011011001001...

10/191=0,00001101011001110011010001000101101100100100001100000100000001010101110001111011010011110001010...

11/191=0,00001110101111100101001100011001011101110100100110110111100111110111111101010100011100001001011...

12/191=0,00010000000101010111000111101101001111000101000001101011001110011010001000101101100100100001100...

13/191=0,00010001011011001001000011000001000000010101011100011110110100111100010100000110101100111001101...

14/191=0,00010010110000111010111110010100110001100101110111010010011011011110011111011111110101010001110...

15/191=0,00010100000110101100111001101000100010110110010010000110000010000000101010111000111101101001111...

16/191=0,00010101011100011110110100111100010100000110101100111001101000100010110110010010000110000010000...

17/191=0,00010110110010010000110000010000000101010111000111101101001111000101000001101011001110011010001...

18/191=0,00011000001000000010101011100011110110100111100010100000110101100111001101000100010110110010010...

19/191=0,00011001011101110100100110110111100111110111111101010100011100001001011000011101011111001010011...

20/191=0,00011010110011100110100010001011011001001000011000001000000010101011100011110110100111100010100...

21/191=0,00011100001001011000011101011111001010011000110010111011101001001101101111001111101111111010101...

22/191=0,00011101011111001010011000110010111011101001001101101111001111101111111010101000111000010010110...

23/191=0,00011110110100111100010100000110101100111001101000100010110110010010000110000010000000101010111...

24/191=0,00100000001010101110001111011010011110001010000011010110011100110100010001011011001001000011000...

25/191=0,00100001100000100000001010101110001111011010011110001010000011010110011100110100010001011011001...

26/191=0,00100010110110010010000110000010000000101010111000111101101001111000101000001101011001110011010...

27/191=0,00100100001100000100000001010101110001111011010011110001010000011010110011100110100010001011011...

28/191=0,00100101100001110101111100101001100011001011101110100100110110111100111110111111101010100011100...

29/191=0,00100110110111100111110111111101010100011100001001011000011101011111001010011000110010111011101...

30/191=0,00101000001101011001110011010001000101101100100100001100000100000001010101110001111011010011110...

31/191=0,00101001100011001011101110100100110110111100111110111111101010100011100001001011000011101011111...

32/191=0,00101010111000111101101001111000101000001101011001110011010001000101101100100100001100000100000...

33/191=0,00101100001110101111100101001100011001011101110100100110110111100111110111111101010100011100001...

34/191=0,00101101100100100001100000100000001010101110001111011010011110001010000011010110011100110100010...

35/191=0,00101110111010010011011011110011111011111110101010001110000100101100001110101111100101001100011...

36/191=0,00110000010000000101010111000111101101001111000101000001101011001110011010001000101101100100100...

37/191=0,00110001100101110111010010011011011110011111011111110101010001110000100101100001110101111100101...

38/191=0,00110010111011101001001101101111001111101111111010101000111000010010110000111010111110010100110...

39/191=0,00110100010001011011001001000011000001000000010101011100011110110100111100010100000110101100111...

40/191=0,00110101100111001101000100010110110010010000110000010000000101010111000111101101001111000101000...

41/191=0,00110110111100111110111111101010100011100001001011000011101011111001010011000110010111011101001...

42/191=0,00111000010010110000111010111110010100110001100101110111010010011011011110011111011111110101010...

43/191=0,00111001101000100010110110010010000110000010000000101010111000111101101001111000101000001101011...

44/191=0,00111010111110010100110001100101110111010010011011011110011111011111110101010001110000100101100...

45/191=0,00111100010100000110101100111001101000100010110110010010000110000010000000101010111000111101101...

46/191=0,00111101101001111000101000001101011001110011010001000101101100100100001100000100000001010101110...

47/191=0,00111110111111101010100011100001001011000011101011111001010011000110010111011101001001101101111...

48/191=0,01000000010101011100011110110100111100010100000110101100111001101000100010110110010010000110000...

49/191=0,01000001101011001110011010001000101101100100100001100000100000001010101110001111011010011110001...

50/191=0,01000011000001000000010101011100011110110100111100010100000110101100111001101000100010110110010...

51/191=0,01000100010110110010010000110000010000000101010111000111101101001111000101000001101011001110011...

52/191=0,01000101101100100100001100000100000001010101110001111011010011110001010000011010110011100110100...

53/191=0,01000111000010010110000111010111110010100110001100101110111010010011011011110011111011111110101...

54/191=0,01001000011000001000000010101011100011110110100111100010100000110101100111001101000100010110110...

55/191=0,01001001101101111001111101111111010101000111000010010110000111010111110010100110001100101110111...

56/191=0,01001011000011101011111001010011000110010111011101001001101101111001111101111111010101000111000...

57/191=0,01001100011001011101110100100110110111100111110111111101010100011100001001011000011101011111001...

58/191=0,01001101101111001111101111111010101000111000010010110000111010111110010100110001100101110111010...

59/191=0,01001111000101000001101011001110011010001000101101100100100001100000100000001010101110001111011...

60/191=0,01010000011010110011100110100010001011011001001000011000001000000010101011100011110110100111100...

61/191=0,01010001110000100101100001110101111100101001100011001011101110100100110110111100111110111111101...

62/191=0,01010011000110010111011101001001101101111001111101111111010101000111000010010110000111010111110...

63/191=0,01010100011100001001011000011101011111001010011000110010111011101001001101101111001111101111111...

64/191=0,01010101110001111011010011110001010000011010110011100110100010001011011001001000011000001000000...

65/191=0,01010111000111101101001111000101000001101011001110011010001000101101100100100001100000100000001...

66/191=0,01011000011101011111001010011000110010111011101001001101101111001111101111111010101000111000010...

67/191=0,01011001110011010001000101101100100100001100000100000001010101110001111011010011110001010000011...

68/191=0,01011011001001000011000001000000010101011100011110110100111100010100000110101100111001101000100...

69/191=0,01011100011110110100111100010100000110101100111001101000100010110110010010000110000010000000101...

70/191=0,01011101110100100110110111100111110111111101010100011100001001011000011101011111001010011000110...

71/191=0,01011111001010011000110010111011101001001101101111001111101111111010101000111000010010110000111...

72/191=0,01100000100000001010101110001111011010011110001010000011010110011100110100010001011011001001000...

73/191=0,01100001110101111100101001100011001011101110100100110110111100111110111111101010100011100001001...

74/191=0,01100011001011101110100100110110111100111110111111101010100011100001001011000011101011111001010...

75/191=0,01100100100001100000100000001010101110001111011010011110001010000011010110011100110100010001011...

76/191=0,01100101110111010010011011011110011111011111110101010001110000100101100001110101111100101001100...

77/191=0,01100111001101000100010110110010010000110000010000000101010111000111101101001111000101000001101...

78/191=0,01101000100010110110010010000110000010000000101010111000111101101001111000101000001101011001110...

79/191=0,01101001111000101000001101011001110011010001000101101100100100001100000100000001010101110001111...

80/191=0,01101011001110011010001000101101100100100001100000100000001010101110001111011010011110001010000...

81/191=0,01101100100100001100000100000001010101110001111011010011110001010000011010110011100110100010001...

82/191=0,01101101111001111101111111010101000111000010010110000111010111110010100110001100101110111010010...

83/191=0,01101111001111101111111010101000111000010010110000111010111110010100110001100101110111010010011...

84/191=0,01110000100101100001110101111100101001100011001011101110100100110110111100111110111111101010100...

85/191=0,01110001111011010011110001010000011010110011100110100010001011011001001000011000001000000010101...

86/191=0,01110011010001000101101100100100001100000100000001010101110001111011010011110001010000011010110...

87/191=0,01110100100110110111100111110111111101010100011100001001011000011101011111001010011000110010111...

88/191=0,01110101111100101001100011001011101110100100110110111100111110111111101010100011100001001011000...

89/191=0,01110111010010011011011110011111011111110101010001110000100101100001110101111100101001100011001...

90/191=0,01111000101000001101011001110011010001000101101100100100001100000100000001010101110001111011010...

91/191=0,01111001111101111111010101000111000010010110000111010111110010100110001100101110111010010011011...

92/191=0,01111011010011110001010000011010110011100110100010001011011001001000011000001000000010101011100...

93/191=0,01111100101001100011001011101110100100110110111100111110111111101010100011100001001011000011101...

94/191=0,01111101111111010101000111000010010110000111010111110010100110001100101110111010010011011011110...

95/191=0,01111111010101000111000010010110000111010111110010100110001100101110111010010011011011110011111...

96/191=0,10000000101010111000111101101001111000101000001101011001110011010001000101101100100100001100000...

97/191=0,10000010000000101010111000111101101001111000101000001101011001110011010001000101101100100100001...

98/191=0,10000011010110011100110100010001011011001001000011000001000000010101011100011110110100111100010...

99/191=0,10000100101100001110101111100101001100011001011101110100100110110111100111110111111101010100011...

100/191=0,10000110000010000000101010111000111101101001111000101000001101011001110011010001000101101100100...

101/191=0,10000111010111110010100110001100101110111010010011011011110011111011111110101010001110000100101...

102/191=0,10001000101101100100100001100000100000001010101110001111011010011110001010000011010110011100110...

103/191=0,10001010000011010110011100110100010001011011001001000011000001000000010101011100011110110100111...

104/191=0,10001011011001001000011000001000000010101011100011110110100111100010100000110101100111001101000...

105/191=0,10001100101110111010010011011011110011111011111110101010001110000100101100001110101111100101001...

106/191=0,10001110000100101100001110101111100101001100011001011101110100100110110111100111110111111101010...

107/191=0,10001111011010011110001010000011010110011100110100010001011011001001000011000001000000010101011...

108/191=0,10010000110000010000000101010111000111101101001111000101000001101011001110011010001000101101100...

109/191=0,10010010000110000010000000101010111000111101101001111000101000001101011001110011010001000101101...

110/191=0,10010011011011110011111011111110101010001110000100101100001110101111100101001100011001011101110...

111/191=0,10010100110001100101110111010010011011011110011111011111110101010001110000100101100001110101111...

112/191=0,10010110000111010111110010100110001100101110111010010011011011110011111011111110101010001110000...

113/191=0,10010111011101001001101101111001111101111111010101000111000010010110000111010111110010100110001...

114/191=0,10011000110010111011101001001101101111001111101111111010101000111000010010110000111010111110010...

115/191=0,10011010001000101101100100100001100000100000001010101110001111011010011110001010000011010110011...

116/191=0,10011011011110011111011111110101010001110000100101100001110101111100101001100011001011101110100...

117/191=0,10011100110100010001011011001001000011000001000000010101011100011110110100111100010100000110101...

118/191=0,10011110001010000011010110011100110100010001011011001001000011000001000000010101011100011110110...

119/191=0,10011111011111110101010001110000100101100001110101111100101001100011001011101110100100110110111...

120/191=0,10100000110101100111001101000100010110110010010000110000010000000101010111000111101101001111000...

121/191=0,10100010001011011001001000011000001000000010101011100011110110100111100010100000110101100111001...

122/191=0,10100011100001001011000011101011111001010011000110010111011101001001101101111001111101111111010...

123/191=0,10100100110110111100111110111111101010100011100001001011000011101011111001010011000110010111011...

124/191=0,10100110001100101110111010010011011011110011111011111110101010001110000100101100001110101111100...

125/191=0,10100111100010100000110101100111001101000100010110110010010000110000010000000101010111000111101...

126/191=0,10101000111000010010110000111010111110010100110001100101110111010010011011011110011111011111110...

127/191=0,10101010001110000100101100001110101111100101001100011001011101110100100110110111100111110111111...

128/191=0,10101011100011110110100111100010100000110101100111001101000100010110110010010000110000010000000...

129/191=0,10101100111001101000100010110110010010000110000010000000101010111000111101101001111000101000001...

130/191=0,10101110001111011010011110001010000011010110011100110100010001011011001001000011000001000000010...

131/191=0,10101111100101001100011001011101110100100110110111100111110111111101010100011100001001011000011...

132/191=0,10110000111010111110010100110001100101110111010010011011011110011111011111110101010001110000100...

133/191=0,10110010010000110000010000000101010111000111101101001111000101000001101011001110011010001000101...

134/191=0,10110011100110100010001011011001001000011000001000000010101011100011110110100111100010100000110...

135/191=0,10110100111100010100000110101100111001101000100010110110010010000110000010000000101010111000111...

136/191=0,10110110010010000110000010000000101010111000111101101001111000101000001101011001110011010001000...

137/191=0,10110111100111110111111101010100011100001001011000011101011111001010011000110010111011101001001...

138/191=0,10111000111101101001111000101000001101011001110011010001000101101100100100001100000100000001010...

139/191=0,10111010010011011011110011111011111110101010001110000100101100001110101111100101001100011001011...

140/191=0,10111011101001001101101111001111101111111010101000111000010010110000111010111110010100110001100...

141/191=0,10111100111110111111101010100011100001001011000011101011111001010011000110010111011101001001101...

142/191=0,10111110010100110001100101110111010010011011011110011111011111110101010001110000100101100001110...

143/191=0,10111111101010100011100001001011000011101011111001010011000110010111011101001001101101111001111...

144/191=0,11000001000000010101011100011110110100111100010100000110101100111001101000100010110110010010000...

145/191=0,11000010010110000111010111110010100110001100101110111010010011011011110011111011111110101010001...

146/191=0,11000011101011111001010011000110010111011101001001101101111001111101111111010101000111000010010...

147/191=0,11000101000001101011001110011010001000101101100100100001100000100000001010101110001111011010011...

148/191=0,11000110010111011101001001101101111001111101111111010101000111000010010110000111010111110010100...

149/191=0,11000111101101001111000101000001101011001110011010001000101101100100100001100000100000001010101...

150/191=0,11001001000011000001000000010101011100011110110100111100010100000110101100111001101000100010110...

151/191=0,11001010011000110010111011101001001101101111001111101111111010101000111000010010110000111010111...

152/191=0,11001011101110100100110110111100111110111111101010100011100001001011000011101011111001010011000...

153/191=0,11001101000100010110110010010000110000010000000101010111000111101101001111000101000001101011001...

154/191=0,11001110011010001000101101100100100001100000100000001010101110001111011010011110001010000011010...

155/191=0,11001111101111111010101000111000010010110000111010111110010100110001100101110111010010011011011...

156/191=0,11010001000101101100100100001100000100000001010101110001111011010011110001010000011010110011100...

157/191=0,11010010011011011110011111011111110101010001110000100101100001110101111100101001100011001011101...

158/191=0,11010011110001010000011010110011100110100010001011011001001000011000001000000010101011100011110...

159/191=0,11010101000111000010010110000111010111110010100110001100101110111010010011011011110011111011111...

160/191=0,11010110011100110100010001011011001001000011000001000000010101011100011110110100111100010100000...

161/191=0,11010111110010100110001100101110111010010011011011110011111011111110101010001110000100101100001...

162/191=0,11011001001000011000001000000010101011100011110110100111100010100000110101100111001101000100010...

163/191=0,11011010011110001010000011010110011100110100010001011011001001000011000001000000010101011100011...

164/191=0,11011011110011111011111110101010001110000100101100001110101111100101001100011001011101110100100...

165/191=0,11011101001001101101111001111101111111010101000111000010010110000111010111110010100110001100101...

166/191=0,11011110011111011111110101010001110000100101100001110101111100101001100011001011101110100100110...

167/191=0,11011111110101010001110000100101100001110101111100101001100011001011101110100100110110111100111...

168/191=0,11100001001011000011101011111001010011000110010111011101001001101101111001111101111111010101000...

169/191=0,11100010100000110101100111001101000100010110110010010000110000010000000101010111000111101101001...

170/191=0,11100011110110100111100010100000110101100111001101000100010110110010010000110000010000000101010...

171/191=0,11100101001100011001011101110100100110110111100111110111111101010100011100001001011000011101011...

172/191=0,11100110100010001011011001001000011000001000000010101011100011110110100111100010100000110101100...

173/191=0,11100111110111111101010100011100001001011000011101011111001010011000110010111011101001001101101...

174/191=0,11101001001101101111001111101111111010101000111000010010110000111010111110010100110001100101110...

175/191=0,11101010100011100001001011000011101011111001010011000110010111011101001001101101111001111101111...

176/191=0,11101011111001010011000110010111011101001001101101111001111101111111010101000111000010010110000...

177/191=0,11101101001111000101000001101011001110011010001000101101100100100001100000100000001010101110001...

178/191=0,11101110100100110110111100111110111111101010100011100001001011000011101011111001010011000110010...

179/191=0,11101111111010101000111000010010110000111010111110010100110001100101110111010010011011011110011...

180/191=0,11110001010000011010110011100110100010001011011001001000011000001000000010101011100011110110100...

181/191=0,11110010100110001100101110111010010011011011110011111011111110101010001110000100101100001110101...

182/191=0,11110011111011111110101010001110000100101100001110101111100101001100011001011101110100100110110...

183/191=0,11110101010001110000100101100001110101111100101001100011001011101110100100110110111100111110111...

184/191=0,11110110100111100010100000110101100111001101000100010110110010010000110000010000000101010111000...

185/191=0,11110111111101010100011100001001011000011101011111001010011000110010111011101001001101101111001...

186/191=0,11111001010011000110010111011101001001101101111001111101111111010101000111000010010110000111010...

187/191=0,11111010101000111000010010110000111010111110010100110001100101110111010010011011011110011111011...

188/191=0,11111011111110101010001110000100101100001110101111100101001100011001011101110100100110110111100...

189/191=0,11111101010100011100001001011000011101011111001010011000110010111011101001001101101111001111101...

190/191=0,11111110101010001110000100101100001110101111100101001100011001011101110100100110110111100111110...

On remarque que le produit du nombre de périodes (2) et de leurs longueurs (95) est égal à 190 et donc au premier -1.