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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Hi;

How would you find the 1000th prime with M if there was no Prime, and there was only PrimeQ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

You need the exact 1000th?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Yeah.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

Then ye will have to loop through them counting as ye go.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

That is the only way?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,258

As you know there is no known formula for generating all the primes in order. So how else? The only trick available is how you iterate to the answer.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But, say you do have the PrimeQ function. Is it possible then to generate it somehow?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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PrimeQ[n] tests n for primality by using Miller Rabin. It does not generate primes.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

I know. The thing is that it is not exactly primes I am interested in, but rather Harshad numbers in base 5.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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What do you want to do with them?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I want to find the 1000th Harshad number in base 5.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Do you have a small test list?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

What kind of test list?

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**bobbym****Administrator**- From: Bumpkinland
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The first few Harshad numbers in base 5 of course.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

These should be correct:

{1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32, 36, 40, 42, 45, 48, 50, 51, 52, 54, 56, 60, 63, 64, 65, 66, 72, 75, 76, 78, 80, 85, 88, 90, 91, 96, 99, 100}

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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```
harshad[n_] := Mod[n, Plus @@ IntegerDigits[n, 5]] == 0;
Select[Range[100], harshad]
```

Try that on a bigger list.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I know how to generate them. I do not know how to get the nth one.

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**bobbym****Administrator**- From: Bumpkinland
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Is there a formula for the nth Harshad humber in any base?

Of course that result can be rigorously obtained, but who cares?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I do not think so. That is why asked for the primes.

If I knew of a way to implement Prime using PrimeQ, it would be easy to implement Harshad using HarshadQ.

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**bobbym****Administrator**- From: Bumpkinland
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What is HarshadQ?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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`HarshadQ[x_, b_] := Mod[x, Plus @@ IntegerDigits[x, b]] == 0`

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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As far as I know there is no other way then checking a subset of the integers using PrimeQ.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Either that or a loop.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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You could cut down the number that you would have to test. or you could download a list of primes. Or you could generate the list yourself. Then you would only have access them by index number.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But, the problem is that it does not extend to other kinds of numbers. As I said, I don't need the nth prime concretely.

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