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Prime Numbers and Number bases: A prime number is a number that is divisible by only two numbers, one and itself. Prime numbers are also an important concept and when well founded and understood learners will not experience problems with factorising. Upon conducting an investigation, Ferguson found an interesting pattern with prime numbers. The table below shows 36 counting numbers arranged in rows of 6. The first column and fifth have most of the numbers as prime numbers except 2 and 3 which are not in those column. 1 7 13 19 25 31 37 43 49 55
Base Ten 3 9 15 21 27 33 39 45 51 57
2 8 14 20 26 32 38 44 50 56
4 10 16 22 28 34 40 46 52 58
5 11 17 23 29 35 41 47 53 59
6 12 18 24 30 36 42 48 54 60
Table 4: Counting Numbers arranged in 6 rows When the same numbers are written in base 6, the pattern is more distinct where the first and fifth column have a general form 6�� ¹ 1. 7, 13, 19 , . . . 6�� + 1
5, 11, 17 , . . . 6đ?‘›đ?‘› − 1
1 11 21 31 41 51 101 111 121 131
2 12 22 32 42 52 102 112 122 132
Base Six 3 13 23 33 43 53 103 113 123 133
4 14 24 34 44 54 104 114 124 134
5 15 25 35 45 55 105 115 125 135
10 20 30 40 50 100 110 120 130 136
Table 5: Numbers in base 6 arranged in 6 rows
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