It
is superfluous to present the numerical system practically the only one used
today in the world. It is also well-known that computing uses a same – binary –
system and that any other system can be set up. If we want to evaluate the
various numeral systems, we could propose some – somewhat subjective –
requirements:
- be easy to
understand and learn,
- be
comfortable for adding numbers,
- be
comfortable for multiplying numbers,
- be able to
quickly identify certain properties of the number.
We
might ask ourselves, how much this makes sense, since we do not really know a
new alternative numeral system. However, in 2019 the situation changed: the
Simi numeral system (SNS) was born!
The rule is that we write down the canonical form of the number (in
descending order of the primes), but with all the smaller prime numbers (with a
zero power), and then we sort the powers one after the other. This sequence is
the number in the Simi numeral system. Eg. 20 = 51×30×22.
Thus, in the Simi system 20 is described: 102. The Fundamental theorem of
arithmetic guarantees that in this form all natural numbers can be written by
one and only one way.
Decimal
|
Simi
|
Decimal
|
Simi
|
1
|
0
|
11
|
10 000
|
2
|
1
|
12
|
12
|
3
|
10
|
13
|
100 000
|
4
|
2
|
14
|
1001
|
5
|
100
|
15
|
110
|
6
|
11
|
16
|
4
|
7
|
1000
|
17
|
1 000 000
|
8
|
3
|
18
|
21
|
9
|
20
|
19
|
10 000 000
|
10
|
101
|
20
|
102
|
What's
the point, what would be the advantage of this numeral system? Cannot overlook
some extraordinary, very useful features of the new system. A huge, unmatched
advantage: multiplying the numbers written in this system (which, let's face
it, especially if the numbers are very large, is a macerated task), can be done
here by simple addition. Remaining in the table above: multiples of 4 and 5 are
20, in the Simi system the same is 2 plus 100, which is 102. One can imagine
how pleased computers would be to multiply millions of times per second for
more serious tasks.
There is a natural consequence of this advantage: raising a number to a square
or any power becomes a simple multiplication. Decimal: 4 on the second 16, on
the Simi system 2 on the second 4. True, adding here is a harder matter.
Continuing with the previous example, the sum of 2 and 100 is 20! Why, who
knows?
But the Simi system has another incredible advantage. Since primes have
appeared, mathematicians have been overly depressed by their ignorance of the
regularity of the appearance of primes, and we have no formula that gives us
the 100th prime, if desired. It is now resolved in this form forever and for
all primes. The hundredth prime is simply 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.
Here is the moment when skeptics can speak up: what do we know from the
above inscription on the hundredth prime? Why, we could answer that, and what
would we know if the same thing were written in decimal? (The debate is by no
means uninteresting, but this is not the moment).
Let's see another interesting chart.
Decimal
|
Simi
|
Decimal
|
Simi
|
2
|
1
|
1
|
0
|
4
|
2
|
10
|
101
|
8
|
3
|
100
|
202
|
16
|
4
|
1 000
|
303
|
32
|
5
|
10 000
|
404
|
64
|
6
|
100 000
|
505
|
128
|
7
|
1 000 000
000
|
606
|
256
|
8
|
10 000 000
000
|
707
|
512
|
9
|
100 000 000
000
|
808
|
1024
|
(10)
|
1
000 000 000 000
|
909
|
The
calculation of the smallest common multiple and the largest common divisor is
also very simple: an operation similar to traditional addition. We write the
two numbers one under the other, and and choose for the result in the first
case the largest, in the second the smallest digit. Incidentally, in this
system, divisibility by a number is no longer an issue.
The Simi system seems to have a serious weakness. How should one
describe a number that has a prime with greater power the 9? Undoubtedly, this
interferes with the incredible convenience of the numerical system, but the
problem is not insolvable. A possible solution would be to put a power greater
than 9 in parentheses. According to this, the infamous Googol number, 10100,
would be described in Simi as (100)0(100).
Otherwise, this technique can also simplify the writing of the hundredth
prime. It would look like this: 1((99) 0).
* * *
