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Topic: Prime Generalization Conjecture
Replies: 48   Last Post: Nov 7, 2017 5:14 PM

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 Richard Heathfield Posts: 134 Registered: 12/22/06
Re: Prime Generalization Conjecture
Posted: Jun 20, 2009 2:45 AM

MeAmI.org said:

> RULE: EVERY PRIME number is exactly
> 1/2 of some other number +1.

2 is a counter-example unless "other number" can mean "same number".

In general, if P = X / 2 + 1, then X = (P - 1) * 2, so your claim is
tantamount to saying that for each prime number there exists some
other number that can be reached by subtracting one from the prime
number and then doubling the result. This leads us to some other
observations of equal interest:

RULE: EVERY PERFECT SQUARE is exactly 1/2 of some other number +1.
RULE: EVERY PERFECT CUBE is exactly 1/2 of some other number +1.
RULE: EVERY FIBONACCI NUMBER is exactly 1/2 of some other number +1.
RULE: EVERY LUCAS NUMBER is exactly 1/2 of some other number +1.
RULE: EVERY INTEGER is exactly 1/2 of some other number +1.

Good solid stuff, but I don't think it's going to win a Fields Medal
any time soon.

--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Forged article? See
http://www.cpax.org.uk/prg/usenet/comp.lang.c/msgauth.php
"Usenet is a strange place" - dmr 29 July 1999

Date Subject Author
6/20/09 MeAmI.org
6/20/09 Richard Heathfield
6/20/09 CBFalconer
6/21/09 Richard Heathfield
6/26/09 MeAmI.org
6/26/09 John H. Guillory
6/26/09 Guest
6/26/09 Richard Heathfield
6/27/09 Guest
6/27/09 Guest
6/27/09 Guest
6/29/09 Peter Nilsson
6/30/09 Guest
6/30/09 Alf P. Steinbach
6/30/09 Richard Heathfield
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6/30/09 Dik T. Winter
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6/30/09 Richard Heathfield
6/30/09 mike
6/30/09 Richard Heathfield
6/30/09 Guest
9/13/13
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7/7/09 Constructive Truth
7/8/09 Alan Morgan
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6/20/09 William Elliot
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