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#1 2013-07-06 04:18:53

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Help with M

Hi;

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#2 2013-07-06 04:36:06

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

You need the exact 1000th?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2013-07-06 04:38:20

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

Yeah.


“Here lies the reader who will never open this book. He is forever dead.

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

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#4 2013-07-06 04:39:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#5 2013-07-06 04:44:17

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

That is the only way?


“Here lies the reader who will never open this book. He is forever dead.

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

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#6 2013-07-06 04:47:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#7 2013-07-06 04:49:49

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#8 2013-07-06 04:51:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

PrimeQ[n] tests n for primality by using Miller Rabin. It does not generate primes.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#9 2013-07-06 04:58:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

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


“Here lies the reader who will never open this book. He is forever dead.

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

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#10 2013-07-06 04:59:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

What do you want to do with them?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#11 2013-07-06 04:59:42

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

I want to find the 1000th Harshad number in base 5.


“Here lies the reader who will never open this book. He is forever dead.

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

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#12 2013-07-06 05:03:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

Do you have a small test list?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#13 2013-07-06 05:08:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

What kind of test list?


“Here lies the reader who will never open this book. He is forever dead.

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

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#14 2013-07-06 05:15:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

The first few Harshad numbers in base 5 of course.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#15 2013-07-06 05:35:02

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

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}


“Here lies the reader who will never open this book. He is forever dead.

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

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#16 2013-07-06 05:38:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

harshad[n_] := Mod[n, Plus @@ IntegerDigits[n, 5]] == 0; 

Select[Range[100], harshad]

Try that on a bigger list.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#17 2013-07-06 05:40:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

I know how to generate them. I do not know how to get the nth one.


“Here lies the reader who will never open this book. He is forever dead.

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

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#18 2013-07-06 05:43:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

Is there a formula for the nth Harshad humber in any base?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#19 2013-07-06 05:45:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

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.


“Here lies the reader who will never open this book. He is forever dead.

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

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#20 2013-07-06 05:49:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

What is HarshadQ?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#21 2013-07-06 05:50:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

HarshadQ[x_, b_] := Mod[x, Plus @@ IntegerDigits[x, b]] == 0

“Here lies the reader who will never open this book. He is forever dead.

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

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#22 2013-07-06 05:58:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

As far as I know there is no other way then checking a subset of the integers using PrimeQ.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#23 2013-07-06 06:04:15

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

Either that or a loop.


“Here lies the reader who will never open this book. He is forever dead.

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

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#24 2013-07-06 06:06:30

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,536

Re: Help with M

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.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Online

#25 2013-07-06 06:10:45

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,380

Re: Help with M

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.


“Here lies the reader who will never open this book. He is forever dead.

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

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