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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Very interesting prblem:

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

We know that:

So

0<Sum<Pi^2/6

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

I'll try to make a program for the sum.

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Here's my program:

```
k = 100000;
ss = 1000;
Print["Initialization Done"];
Do[prt[i] = Prime[i], {i, 1, k}];
Print["Prime Geneneration Done"];
Do[prtsq[i] = prt[i]*prt[i], {i, 1, k}];
Print["Squaring Done"];
Do[thearr[i] = 1/prtsq[i], {i, 1, 100000}];
Print["Factorising Done"];
sum = 0;
Do[sum += N[thearr[i], ss], {i, 1, 100000}];
Print["Sum = ", sum];
```

And here's what I get for the sum:

0.4522473688277700954422164277522326096645066956889359406373748543156987039966

525643794108225095161389758244363445339660776113109242885808492718205416638194

526958800379786519866057949036856229177825278987902389864970540352844167196863

834688645075159015805935496856212223538491039364902103635445065361656745970932

905021125274435235568533828552570131338540212094414196757580439057169807537575

899440924188480149221835203239871132457344235369007243117411236106046262308444

576868350724155932530725321698618605264299442562165096782086212268498382688102

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Is this sum a irrational number?

Is It transcedent?

Can we compute Prime[n] from it?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

I get everything except the N and the ss usage.

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

In Mathematica the "N(number,precise)" function gives the number with precisedigits after the demical point.

Here's an example:

N[Pi,2]=3.14

N[Pi,4]=3.1415

ss is the precise. Because ss=1000 we can be sure that more than 100 digits or this number are correct.

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

And if Prime[] returns 0 if not prime, then why don't you get divide by zero error?

Tell me about Prime[]

Does prime return infinitywhen not prime?

**igloo** **myrtilles** **fourmis**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

Maybe we could it "Krassi's Number"

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

For John, not, PrimeQ[] is for testing whatever a number is prime.

Prime[n] gives the n-th pime number:

Prime[1]=2

Prime[2]=3

Prime[3]=5

...

IPBLE: Increasing Performance By Lowering Expectations.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

And for rob-ya, it's actually a great idea to call it "Krassi's number". But it's not os scientific as "Geogiev's constant".

IPBLE: Increasing Performance By Lowering Expectations.

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Okay, now the program makes sense, thanks a lot.

**igloo** **myrtilles** **fourmis**

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**God****Member**- Registered: 2005-08-25
- Posts: 59

Maybe the solution lies in the infinite pi-notation format of the reimann zeta function

After all, problems are a lot cooler to solve by hand than to approximate with computer

*Last edited by God (2006-03-02 11:18:20)*

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

What is that infinite pi-notation?

Can you explain it...

Simply?

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

can.t locate bug in k.h. program.

but pi squrd over six is just shy of ten over six.

**igloo** **myrtilles** **fourmis**

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 102,812

Hi;

There seems to be a slight inaccuracy in the determination of that constant. Correct to 100 places is

0.4522474200410654985065433648322479341732313432398924217364189303511650273639108744489575443549068582...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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