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• I have found tabulary that a perfect no. -1 or -3 is never a prime. but I can t not find mathmatical solution to that. Another related quesstion is that every
Message 1 of 8 , Feb 9, 2001
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I have found tabulary that a perfect no. -1 or -3 is never a prime.
but I can't not find mathmatical solution to that.

Another related quesstion is that every perfect no. can be written
as perfect no. PN = 2m^2+3m+1 where m is odd
and if so PN=2^n - m-1
why is this so ?
• ... 6 is perfect, but 6-1 is prime. +-----------------------------------------------------------+ ...
Message 2 of 8 , Feb 9, 2001
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At 06:59 PM 2/9/2001 +0000, habibnajafi@... wrote:
>I have found tabulary that a perfect no. -1 or -3 is never a prime.
>but I can't not find mathmatical solution to that.

6 is perfect, but 6-1 is prime.

+-----------------------------------------------------------+
| Jud McCranie |
| |
| Think recursively( Think recursively( Think recursively)) |
+-----------------------------------------------------------+
• 6 is also a special case. It s the only perfect number whose power of 2 component (the other being the Mersenne prime) is itself prime. So he may still be
Message 3 of 8 , Feb 9, 2001
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6 is also a special case. It's the only perfect number whose power of 2
component (the other being the Mersenne prime) is itself prime. So he may
still be right.

-- Barubary

----- Original Message -----
From: "Jud McCranie" <jud.mccranie@...>
To: <habibnajafi@...>
Sent: Friday, February 09, 2001 13:30

> At 06:59 PM 2/9/2001 +0000, habibnajafi@... wrote:
> >I have found tabulary that a perfect no. -1 or -3 is never a prime.
> >but I can't not find mathmatical solution to that.
>
> 6 is perfect, but 6-1 is prime.
>
> +-----------------------------------------------------------+
> | Jud McCranie |
> | |
> | Think recursively( Think recursively( Think recursively)) |
> +-----------------------------------------------------------+
>
>
>
>
> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
> The Prime Pages : http://www.primepages.org
>
>
>
• ... These numbers are less likely to be prime, since all perfect numbers end in 6 or 8 in decimal, making one value or the other divisible by 5. Another
Message 4 of 8 , Feb 9, 2001
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On Fri, 09 Feb 2001 16:30:04 -0500, Jud McCranie wrote:

>At 06:59 PM 2/9/2001 +0000, habibnajafi@... wrote:
>>I have found tabulary that a perfect no. -1 or -3 is never a prime.
>>but I can't not find mathmatical solution to that.
>
>6 is perfect, but 6-1 is prime.

These numbers are less likely to be prime, since all perfect numbers
end in '6' or '8' in decimal, making one value or the other divisible
by 5.

Another counterexamples, of course, is 6-3.

I was unable to find any primes using pfgw, but it seems to tend to
discard smaller numbers by factoring them to themselves, which I am
not sure how to get around.

Nathan
• In a message dated 2/9/01 6:11:33 PM Eastern Standard Time, barubary@home.com ... 6 is also a special case since it is the only case where the
Message 5 of 8 , Feb 9, 2001
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In a message dated 2/9/01 6:11:33 PM Eastern Standard Time, barubary@...
writes:

> 6 is also a special case. It's the only perfect number whose power of 2
> component (the other being the Mersenne prime) is itself prime. So he may
> still be right.
>
>

6 is also a special case since it is the only case where the
PN=2^(p-1)*(2^p-1) involves an even prime p = 2.

[Non-text portions of this message have been removed]
• ... Hi Nathan, The latest PFGW Dev version handles these correctly; get it from http://groups.yahoo.com/group/primeform/files/PFGW-dev-20010125.zip Michael.
Message 6 of 8 , Feb 10, 2001
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> I was unable to find any primes using pfgw, but it seems to tend to
> discard smaller numbers by factoring them to themselves, which I am
> not sure how to get around.

Hi Nathan,

The latest PFGW Dev version handles these correctly; get it from
http://groups.yahoo.com/group/primeform/files/PFGW-dev-20010125.zip

Michael.
• Let a,b,c be consecutive natural numbers, where a  1 (a*c)-b appears to offer a greater density of primes than the norm; why? [Non-text portions of this
Message 7 of 8 , Jun 5, 2008
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Let a,b,c be consecutive natural numbers, where a >1
(a*c)-b appears to offer a greater density of primes than the norm; why?

[Non-text portions of this message have been removed]
• From: Bob Gilson ... why? Call them n-1, n, and n+1 instead of a, b and c. Then a*c-b is n^2 - n - 1. This is never divisible by 2, so produces twice the
Message 8 of 8 , Jun 5, 2008
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From: Bob Gilson
> Let a,b,c be consecutive natural numbers, where a >1
> (a*c)-b appears to offer a greater density of primes than the norm;
why?

Call them n-1, n, and n+1 instead of a, b and c. Then a*c-b is
n^2 - n - 1. This is never divisible by 2, so produces twice the
primes "as usual." It is never divisible by 3, so that gives a
factor of 3/2. Nor by 7, that gives 7/6. So with these alone
we expect 3.5 times the usual number.

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