## RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it any easier.

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• Matteo, ... An expression (e.g. 2n+1) represents a set S if every number from set S can be written in the form prescribed by the expression. It s not necessary
Message 1 of 16 , Aug 3 3:08 PM
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Matteo,

> > Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,
> > consequently, it represents all primes with the exception of 2 and 3. This
> > is where it differs from your form 3n+2+4, which guarantees the "not
> > divisible by 3" condition, but not the "is odd" one.
>
> I don't thing i understand very well what you're saying about 6n+/-1 that
> should represent all primes.

An expression (e.g. 2n+1) represents a set S if every number from set S
can be written in the form prescribed by the expression. It's not
necessary for all the numbers of that form to belong to set S.

For example, the form 2n+1 represents all odd integers. Thus, it can also
be used to represent each and every odd prime, odd square or odd perfect
number -- since all of these are just subsets of the set of odd numbers.

Peter
• Peter Thanks for your comment. I admit I am wrong technically in that since 2 is the only even prime, I usually skirt around that issue by always prefacing
Message 2 of 16 , Aug 3 4:00 PM
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Peter Thanks for your comment. I admit I am wrong technically in that since
2 is the only even prime, I usually skirt around that issue by always
prefacing my remarks by stating ³in the set of odd numbers only,² which I
neglected to do in this case. I do that because prime 2 always obfuscates
the issue, as it is doing in this very instance. Thanks for your interest.
Marty

From: Matteo Mattsteel Vitturi <mattsteel@...>
Date: Tue, 3 Aug 2010 23:25:54 +0200
Subject: RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it
any easier.

Peter,

> > Folks out there including yourself and Lelio don't seem to understand

> > that 6n+/-1 represents ALL integers that are not multiples of 3, so of

> > course every single prime to infinity is either 6n+1, or 6n-1,

>

> Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,

> consequently, it represents all primes with the exception of 2 and 3. This

> is where it differs from your form 3n+2+4, which guarantees the "not

> divisible by 3" condition, but not the "is odd" one.

>

I don't thing i understand very well what you're saying about 6n+/-1 that
should represent all primes.
When n=20 then 6n-1=119 and 6n+1=121 and both aren't primes since 121 is
11x11 and 119 is 7x17.

Matteo.

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• Peter Thanks for your comment. I admit I am technically wrong in that since 2 is the only even prime, I usually skirt around that special case by always
Message 3 of 16 , Aug 3 9:39 PM
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Peter Thanks for your comment. I admit I am technically wrong in that
since 2 is the only even prime, I usually skirt around that special case by
always prefacing my remarks with ³in the set of odd numbers only,² which
I neglected to do, much to my regret since I am getting flak from around
the world. I do that because prime 2 always obfuscates the issue, as it is
doing in this very instance.
So, to correct, the locus for ALL primes except 2 is 6n+1 or 6n-1,
which of course is not to say that all 6n+-1 are prime. Another way to
define 6n+-1 is 3n+2+4, where both are one and the same. The distinction I
am making is that 3n+2+4 is descriptive (to me) of all non-multiples >3 to
infinty, while 6n+-1, makes it appear that there is something profound and
face from the very outset as 3n+2+4. If you look at in this light, it will
all come together. Thus, the search for a pattern in 6n+1-1 is all in vain.
A list of prime numbers (go primes.utm.edu ) has provided this information
forever. Thanks for your interest. Regards. Marty

From: Peter Kosinar <goober@...>
Date: Wed, 4 Aug 2010 00:08:38 +0200 (CEST)
To: Matteo Mattsteel Vitturi <mattsteel@...>
Subject: RE: [PrimeNumbers] Re: Easy formula for next prime... cant make it
any easier.

Matteo,

> > Wrong. 6n+/-1 represents all -odd- integers not divisible by 3 and,
> > consequently, it represents all primes with the exception of 2 and 3. This
> > is where it differs from your form 3n+2+4, which guarantees the "not
> > divisible by 3" condition, but not the "is odd" one.
>
> I don't thing i understand very well what you're saying about 6n+/-1 that
> should represent all primes.

An expression (e.g. 2n+1) represents a set S if every number from set S
can be written in the form prescribed by the expression. It's not
necessary for all the numbers of that form to belong to set S.

For example, the form 2n+1 represents all odd integers. Thus, it can also
be used to represent each and every odd prime, odd square or odd perfect
number -- since all of these are just subsets of the set of odd numbers.

Peter

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