perplexus.info :: Probability : Never prime! (3)

Never prime! (3) (Posted on 2011-02-25)

The value of the smallest positive base ten integer that cannot be changed into a prime by changing a single digit was determined in Never prime!.

M denotes the smallest value of a base N positive integer that cannot be changed into a prime by changing a single digit.

For the values of N drawn at random between 51 and 100 inclusively, determine the probability that the first digit of M (reading left to right) is 3.

Note: N is a positive integer and, M cannot contain any leading zero, and the first digit of M (reading left to right) cannot be changed to a zero.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

Comment 1 of 1

Continuing from the work done on Never Prime! (2), the following numbers are, to the best of my knowledge, the smallest desired values for base 51 to 100.

51 31416 {12, 4, 0}

52 31408 {11, 32, 0}

53 107378 {38, 12, 0}

54 89694 {30, 41, 0}

55 31405 {10, 21, 0}

56 102704 {32, 42, 0}

57 31407 {9, 38, 0}

58 173362 {51, 31, 0}

59 107380 {30, 50, 0}

60 134520 {37, 22, 0}

61 173362 {46, 36, 0}

62 155930 {40, 35, 0}

63 155925 {39, 18, 0}

64 188032 {45, 58, 0}

65 155935 {36, 59, 0}

66 188034 {43, 11, 0}

67 332320 {1, 7, 2, 0}

68 155924 {33, 49, 0}

69 360663 {1, 6, 52, 0}

70 370300 {1, 5, 40, 0}

71 370265 {1, 2, 32, 0}

72 338040 {65, 15, 0}

73 155928 {29, 19, 0}

74 370296 {67, 46, 0}

75 155925 {27, 54, 0}

76 370272 {64, 8, 0}

77 155925 {26, 23, 0}

78 155922 {25, 49, 0}

79 370273 {59, 26, 0}

80 576800 {1, 10, 10, 0}

81 155925 {23, 62, 0}

82 1053864 {1, 74, 60, 0}

83 370263 {53, 62, 0}

84 370272 {52, 40, 0}

85 360655 {49, 78, 0}

86 1313478 {2, 5, 51, 0}

87 370272 {48, 80, 0}

88 927872 {1, 31, 72, 0}

89 1140001 {1, 54, 82, 0}

90 492120 {60, 68, 0}

91 370279 {44, 65, 0}

92 1098848 {1, 37, 76, 0}

93 360654 {41, 65, 0}

94 370266 {41, 85, 0}

95 1313470 {1, 50, 51, 0}

96 370272 {40, 17, 0}

97 1357224 {1, 47, 24, 0}

98 1357202 {1, 43, 31, 0}

99 1444311 {1, 48, 36, 0}

100 1671800 {1, 67, 18, 0}

Of those 50 numbers, 20 have a first digit of 3. That gives a probability of 0.4 or 40%.

Posted by Justin on 2011-03-02 09:58:41

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