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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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: 90,527

You need the exact 1000th?

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

Yeah.

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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: 90,527

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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: 90,527

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.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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?

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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?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

What kind of test list?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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The first few Harshad numbers in base 5 of course.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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.

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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
- Registered: 2009-04-12
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Is there a formula for the nth Harshad humber in any base?

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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
- Registered: 2009-04-12
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What is HarshadQ?

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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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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Either that or a loop.

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**bobbym****Administrator**- From: Bumpkinland
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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.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

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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