Numbers in Other Bases are Belong to Us

[sweety439]

Originally Posted by R2357

I noticed that if we classify the bases according to how efficient they are to identify at once (by the last digit) composites, base 10 is "quite" good, but not the best!
Not even up to 10, as base 6 is better.

I saw above that some wish a shifting to base 12, which is better than 10, but it's on the same rank as 6.

If we want to change our number system, as we already have existing bases, why not change for an even more efficient, how about 30, (I don't know if we have enough symbols for base 210).

Dozenal is the best base!!! See page https://dozenal.fandom.com/wiki/10 and the links at the bottom of this page.

[LaurV]

Originally Posted by sweety439

Dozenal is the best base!!!

Actually, I believe that 60060 is the best base. It is divisible by a lot of small numbers, and it fits in 16 bits so that you can use an uint32 to multiply two digits in a single clock cycle without loss of precision on many of the 32-bit processors nowadays (like ARM and Cortex M).

Hihi.
[/trolling]

[retina]

Originally Posted by R2357

(I don't know if we have enough symbols for base 210).

There are plenty of symbols available. One look at the Unicode tables will convince you that a lack of symbols is not the problem here.

ETA: Even LaurV's base 60060 can be accommodated with Unicode symbols. If one has the necessary desire.

[S485122]

Originally Posted by LaurV

Actually, I believe that 60060 is the best base. It is divisible by a lot of small numbers, and it fits in 16 bits so that you can use an uint32 to multiply two digits in a single clock cycle without loss of precision on many of the 32-bit processors nowadays (like ARM and Cortex M).

Hihi.
[/trolling]

Euh ... to fit in 16 bits it would be 30030 (13#).

Jacob

It it ain't you trolling, but them dozenalers. ;-)
They forget that most humans have 5 digits and two hands, that the supposed benefits of base 12 don't weight up to having (almost) the whole world change their way of counting, and having to replace (almost) all things displaying numbers...

[retina]

Originally Posted by S485122

Euh ... to fit in 16 bits it would be 30030 (13#).

2^16 = 65536, right?

[LaurV]

Originally Posted by S485122

Euh ... to fit in 16 bits it would be 30030 (13#).

Nope. 16 bits can store a number between 0 and 65535. Why should you bother with negatives? In fact, I explicitly mentioned uint32. Please read again. Here "u" in front of "int" stands for "unsigned".
And for the 13# part, you would need to multiply it by 2, because mersenne classes for k need to be multiple of 4 to have q=2kp+1 be 1 or 7 (mod 8), see discussions in this thread. That's why mfaktc uses 4620 classes (2*11#) and not 2310. This way, you can very fast discard half of the filtered candidates (those which are 3 or 5 (mod 8)) without any test (because they will all be in the same class, which you just ignore), getting things done much faster.

[S485122]

Originally Posted by retina

2^16 = 65536, right?

Originally Posted by LaurV

Nope. 16 bits can store a number between 0 and 65535. Why should you bother with negatives? In fact, I explicitly mentioned uint32. Please read again. Here "u" in front of "int" stands for "unsigned".
And for the 13# part, you would need to multiply it by 2, because mersenne classes for k need to be multiple of 4 to have q=2kp+1 be 1 or 7 (mod 8), see discussions in this thread. That's why mfaktc uses 4620 classes (2*11#) and not 2310. This way, you can very fast discard half of the filtered candidates (those which are 3 or 5 (mod 8)) without any test (because they will all be in the same class, which you just ignore), getting things done much faster.

Oups : it is so obvious ... now.

Jacob

Instead of thinking I mishandled a program : I tried first with another number 2*2*2*3*3*5*7*11*13 But must have typed in something else, then deduced from the 18 bits that your number would use more than 16 while 655536 is a known quantity so closely associated with 16 bits ;-)

I'd wish somebody deleted that stupid post of mine.

[Nick]

We all have moments like that!

[LaurV]

Originally Posted by S485122

I'd wish somebody deleted that stupid post of mine.

Buddy, you are not alone. All of us have some brain farts regularly, I for sure lead the list and these guys here are all eager and waiting to byte me when that happens. And I, them, haha. But that's the good part of science, when you make mistakes (general you), others correct you, and you realize the mistake, and you learn something from it. Then, next time you know, and can come with something better, therefore helping others in return.

[S485122]

Originally Posted by LaurV

Buddy, you are not alone. All of us have some brain farts regularly, I for sure lead the list and these guys here are all eager and waiting to byte me when that happens. And I, them, haha. But that's the good part of science, when you make mistakes (general you), others correct you, and you realize the mistake, and you learn something from it. Then, next time you know, and can come with something better, therefore helping others in return.

The problem in this case is that I didn't learn anything new about powers of two or numerical representations. It is just a case of not using my brain correctly.
You could say I learned that my brain can "fart", but that is something I know and despair ;-) about since a very long time. Also this brain fart is now saved for posterity :-D

But thanks for your and Nick's nice answers !

Jacob

[xilman]

Originally Posted by S485122

They forget that most humans have 5 digits and two hands, that the supposed benefits of base 12 don't weight up to having (almost) the whole world change their way of counting, and having to replace (almost) all things displaying numbers...

See my avatar.