Having spent some time to study Prime numbers in the past few days, I find that we can easily identify Prime numbers within 120 if we change our numbering system to base 6.

To work with base 6, we arrange number in 6 columns and labelled them sequentially as 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20 etc.

Then:

all numbers that ends with digit 0 are divisible by 6 (Rule #1);

all numbers with last digit divisible by 2 are divisible by 2 (Rule #2);

all numbers with last digit divisible by 3 are divisible by 3 (Rule #3);

all numbers whose Q-sum (i.e. sum of all digits) divisible by 5 are divisible by 5 (Rule #4);

all numbers whose A-sum (i.e. sum of odd digits minus even digits) divisible by 11 on base 6 (i.e. 7 on base 10) are divisible by 7 (Rule #5)

After having eliminated the above, the remaining numbers are Prime numbers on base 6. When converted back to base 10, they form the complete list of Prime numbers within 120.

1=decimal 1

2=decimal 2

3=decimal 3

4(#2)

5=decimal 5

10(#1)

11=1x6+1=decimal 7

12(#2)

13(#3)

14(#2)

15=1x6+5=decimal 11

20(#1)

21=2x6+1=decimal 13

22(#2)

23(#3)

24(#2)

25=2x6+5=decimal 17

30(#1)

31=3x6+1=decimal 19

32(#2)

33(#3)

34(#2)

35=3x6+5=decimal 23

40(#1)

41(#4)

42(#2)

43(#3)

44(#2)

45=4x6+5=decimal 29

50(#1)

51=5x6+1=decimal 31

52(#2)

53(#3)

54(#2)

55(#4)

100(#1)

101=1x36+0x6+1=decimal 37

etc...

Nonsense, afterall.

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