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

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• Peter, ... 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
Message 1 of 16 , Aug 3, 2010
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.

[Non-text portions of this message have been removed]
• 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 2 of 16 , Aug 3, 2010
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 3 of 16 , Aug 3, 2010
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.

[Non-text portions of this message have been removed]

[Non-text portions of this message have been removed]
• 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 4 of 16 , Aug 3, 2010
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
revealing about this infinite set when in fact it has been staring us in the
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

[Non-text portions of this message have been removed]
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