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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

The equation is given as follows:

Example:

n=1, Ps=1+1=2

n=3, Ps=1-2-3+1*2*3=2

n=5, Ps=1-2-3-4-5+1*2*3*4*5=107

n=6, Ps=1-2-3-4-5-6+1*2*3*4*5*6=701

n=10, Ps=1-2-3-4-5-6-7-8-9-10+1*2*3*4*5*6*7*8*9*10=3628747

n=13, Ps=1-2-3-4-5-6-7-8-9-10-11-12-13+1*2*3*4*5*6*7*8*9*10*11*12*13=6227020711

n=26, Ps=1-2-3-4-5-6-7-8-9-10-11-12-13-..-26+1*2*3*4*5*6*7*8*9*10*11*12*13*..26=403291461126605635583999651

*Last edited by Stangerzv (2014-04-12 12:40:17)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,657

Hi Stangerzv;

What is the first equation for?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

Hi bobbym

Sorry there is a mistake with the minus sign, I've edited it. Basically 1-2-3-..n=2-(1+2+3) and 1*2*..n=n!, the first equation is the generalize equation for the primes.

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

Another version of the prime yields 6 primes so far

n=2, Ps=-1+2+1*2=3

n=6, Ps=-1+2+3+4+5+6+1*2*3*4*5*6=739

n=10, Ps=-1+2+3+4+5+6+7+8+9+10+1*2*3*4*5*6*7*8*9*10=3628853

n=14, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+1*2*3*4*5*6*7*8*9*10*11*12*13*14=87178291303

n=22, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+..+22+1*2*3*4*5*6*7*8*9*10*11*12*13*14*..*22=1124000727777607680251

n=26, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+..+26+1*2*3*4*5*6*7*8*9*10*11*12*13*14*..*26=403291461126605635584000349

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

There are only three double primes by combining the equations above. The double prime generalize equation is gives as follows:

n=6, Ps=701, 739

n=10, Ps=3628747, 3628853

n=26, Ps=403291461126605635583999651, 403291461126605635584000349

*Last edited by Stangerzv (2014-04-12 13:54:25)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,657

Hi;

For the equation:

n = 26 is the highest one for n ≤ 2000

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

Hi bobbym

I have done with the calculation for

n=26 is the highest prime for n ≤ 5000.

*Last edited by Stangerzv (2014-04-13 11:34:13)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,657

Hi;

How far have you gone with that one?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

Hi bobbym

I haven't tried it yet but for

n=26 gives the highest prime for n≤ 8000

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,657

Might not be any after n = 26...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 227

Hi bobym

For

n=26 gives the highest prime for for n ≤ 4000.

*Last edited by Stangerzv (2014-04-14 11:35:06)*

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