DaveC426913
Valued Senior Member
I'm having a hard time following your logic.
So, are you saying 21 is prime?
[11111]+[11111]+[11111]+[11111]+1 5+5+5+5+1=21
Numbers and Logic
- Thread starter arfa brane
- Start date
So, are you saying 21 is prime?
[11111]+[11111]+[11111]+[11111]+1 5+5+5+5+1=21
DaveC426913
Valued Senior Member
Right. Because you are dividing by two. Or more.
So you're not using a primitive counting system - you're still using numbers greater than 1 - you're just not calling them by their names.
If there are exactly two identical sets that equal the number, then the number is divisible by 2.
If there are exactly three identical sets that equal the number, then the number is divisible by 3.
And so on.
Since a prime is only divisible by 1 and itself, it can't be divisible by 2 or 3 or 4 or any number less than itself.
For example, take the number 12:
12 = [111111] + [111111], so divisible by 2.
12 = [1111] + [1111] + [1111], so divisible by 3.
12 = [111] + [111] + [111] + [111], so divisible by 4.
12 = [11] + [11] + [11] + [11] + [11] + [11], so divisible by 6.
It is not divisible by 5, because there are no "groups" we could use to make 5 sets (we'd need groups containing between 2 and 3 "1"s).
12 = [111111] + [111111], so divisible by 2.
12 = [1111] + [1111] + [1111], so divisible by 3.
12 = [111] + [111] + [111] + [111], so divisible by 4.
12 = [11] + [11] + [11] + [11] + [11] + [11], so divisible by 6.
It is not divisible by 5, because there are no "groups" we could use to make 5 sets (we'd need groups containing between 2 and 3 "1"s).
60 gives you 5 sets , of twelve .
Is 60 the same number as 12, river? Work it out and get back to me when you have an answer.
arfa brane
The definition of a prime is so scant it cannot be used to find them.
The definition of the non primes is enough to find them, then remove them.
Put down the sequence 1 thru 100.
Remove the powers of 2,_4, 6, 8 etc.
Remove the powers of 3,_6,9,12 etc.
Remove the powers of 4_8,12,16 etc.
Etc.
The primes will be left standing.
The definition of a prime is so scant it cannot be used to find them.
The definition of the non primes is enough to find them, then remove them.
Put down the sequence 1 thru 100.
Remove the powers of 2,_4, 6, 8 etc.
Remove the powers of 3,_6,9,12 etc.
Remove the powers of 4_8,12,16 etc.
Etc.
The primes will be left standing.
[OFF TOPIC]
Did Newton's calculus have to overcome a hurdle by the introduction of a limit because people were reluctant with infinities and a number approaching 0 as it encroached an a division by 0?
Did Newton's calculus have to overcome a hurdle by the introduction of a limit because people were reluctant with infinities and a number approaching 0 as it encroached an a division by 0?
Formulas for primes
There is no known efficient formula for primes. For example, there is no non-constant polynomial, even in several variables, that takes only prime values.[52] However, there are numerous expressions that do encode all primes, or only primes. One possible formula is based on Wilson's theorem and generates the number 2 many times and all other primes exactly once.[53] There is also a set of Diophantine equations in nine variables and one parameter with the following property: the parameter is prime if and only if the resulting system of equations has a solution over the natural numbers. This can be used to obtain a single formula with the property that all its positive values are prime.[52]
Other examples of prime-generating formulas come from Mills' theorem and a theorem of Wright. These assert that there are real constants A > 1 and μ such that
are prime for any natural number n in the first formula, and any number of exponents in the second formula.[54] Here ⌊ ⋅ ⌋ represents the floor function, the largest integer less than or equal to the number in question. However, these are not useful for generating primes, as the primes must be generated first in order to compute the values of A or μ.[52]
--https://en.wikipedia.org/wiki/Prime_number
There is no known efficient formula for primes. For example, there is no non-constant polynomial, even in several variables, that takes only prime values.[52] However, there are numerous expressions that do encode all primes, or only primes. One possible formula is based on Wilson's theorem and generates the number 2 many times and all other primes exactly once.[53] There is also a set of Diophantine equations in nine variables and one parameter with the following property: the parameter is prime if and only if the resulting system of equations has a solution over the natural numbers. This can be used to obtain a single formula with the property that all its positive values are prime.[52]
Other examples of prime-generating formulas come from Mills' theorem and a theorem of Wright. These assert that there are real constants A > 1 and μ such that
are prime for any natural number n in the first formula, and any number of exponents in the second formula.[54] Here ⌊ ⋅ ⌋ represents the floor function, the largest integer less than or equal to the number in question. However, these are not useful for generating primes, as the primes must be generated first in order to compute the values of A or μ.[52]
--https://en.wikipedia.org/wiki/Prime_number
If we use "division logic" so we get a relation: does/does not divide (where what is meant is division without remainder) then the logic in primes looks a bit more familiar. This 'Boolean' relation exists whether we want to use it in some formal description or not.
Curiously, it isn't hard to find (i.e. count) the number of primes less than a given number, it is hard to find the actual primes because division (not a set of divisors), is necessarily algorithmic.
Curiously, it isn't hard to find (i.e. count) the number of primes less than a given number, it is hard to find the actual primes because division (not a set of divisors), is necessarily algorithmic.
Speakpigeon
Valued Senior Member
I hope you mean "which of course, doesn't mean someone else CAN'T use it", right?
Gee, you need a Frenchman to correct your English!
Still, I see you've been somewhat impressed by my discussion of why there is no science of logic. Not all in vain, then.
It's not essentially a deductive logic problem. There is no general algorithm for proving theorems. The method humans use for proving theorem relies on deductive logic but deductive logic is only one part of the method, and the other part can't be dispensed with.
It's the definition. You have to start with one and you always start with the definition. But then deductive logic can't tell you on its own what would be the general formula for finding primes.
Sure we need more logic, you're making my point, but it wouldn't be enough anyway. We would need something else altogether, something of a very different nature, not theoretical and abstract: brain power. Raw brain power.
Humans are not good at thinking. It's costly in terms of energy and time and if we all did it we would not be here at all to talk about it because humans wouldn't have the time to do the basic chores of life which are necessary for their survival and therefore to our existence today. This explains why there are relatively few thinkers and also therefore why we remember them. And nothing bad about not being a thinker. Most are crap anyway and we only remember the good ones and they are even less many. It's mostly a thankless job.
So, mathematicians do their best but they don't have the raw brain power anyway and most of them are not even good mathematicians. Most so-called mathematicians just repeat all their lives what they've learnt at "school", barely making a scratch on the Great Book of mathematics. So, instead, people do what they know, algorithms! Alleluia. Thinking? No, thanks, too bloody exhausting. A thankless job.
But why don't you do it? You've identified the problem. All that remains for you to do is to think about it and solve it. You don't need much logic. You just need brain power. You just need to think. You know, the thing which it is just so exhausting to do?
Go on, do it.
EB
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This is bullshit.
You mean, we can design algorithms without thinking about it? Sounds like complete . . . bullshit.
Ah yes, condescension. The last refuge of the intellectually challenged.