B71 #26: Method to sieve for Prime

Article #24 talked about Learning Disabilities. You may wish to know that Hong Kong has a "Society for Learning Disabilities" with website: www.sld2000.com. The name of the Society has now been changed to "Distinguished Learning Society" because the helpful learning method can shed new light, on gifted as well as less gifted ones.

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.