Prime Numbers - Base Patterns Page 2
ADVERTISEMENT
1
2
3Here are the first sixteen numbers in base four:
1
2
3 10
11
12
13 20
21
22
23 30
31
32
33 100
101
102 103 110
111
112 113 120
121
122 123 130
131
132 133 200
and the first six dozen in base twelve:
1
2
3
4
5
6
7
8
9
7
8 10
11
12
13 14 15 16 17 18 19 17 18 20
21
22
23 24 25 26 27 28 29 27 28 30
31
32
33 34 35 36 37 38 39 37 38 40
41
42
43 44 45 46 47 48 49 47 48 50
51
52
53 54 55 56 57 58 59 57 58 60
(Note that we use 7 for ten and 8 for eleven in base twelve).
You have to go to 6n±1 to arrive at the minimum set to contain all primes (except 2
and 3) whilst leaving out the unwanted odd multiples of 3. The form 4n±1 gener-
ates an unnecessarily large quantity of numbers. The point is that the primes are
tied to locations about the multiples of six, but do not attain their clearest possible
labels until expressed in base twelve, which is the least base in which all primes ter-
minate with 1 or a prime digit (5, 7 or 8) for those greater than 3.
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education