
Re: Prime Generalization Conjecture
Posted:
Jun 20, 2009 11:01 AM


Oh I see you're not answering...(Revised)
Musatov wrote: > On Jun 20, 4:06 am, Musatov <marty.musa...@gmail.com> wrote: > > On Jun 20, 12:13 am, William Elliot <ma...@rdrop.remove.com> wrote: > > > > > On Fri, 19 Jun 2009, MeAmI.org wrote: > > > > RULE: EVERY PRIME number is exactly > > > > 1/2 of some other number +1. > > > > > So what? For all x, x = (2x  2)/2 + 1. > > > > > Trivial rule. > > > Every integer (rational number, real number, complex number) is half > > > of some integer (resp. rational number, real number, complex number) > > > plus one. > > > > > Exercise. How many primes are half of some prime plus one?
None. Half of a prime number is not a whole number. (Except 2, in which case the whole number is 1). 17/2=8.5+1=9.5 (NP).
So we have the result:
RULE: No prime number greater than two is 1/2 another prime number plus one.
But perhaps this is what you meant.
Inverse/Additive prime property per Musatov: (below)
RULE: EVERY PRIME number greater than 2 is twice a number +1. 3=1*2+1 5=2*2+1 7=3*2+1 11=5*2+1 13=6*2+1 17=8*2+1 19=9*2+1 23=11*2+1 29=14*2+1 31=15*2+1 37=18*2+1 41=20*2+1 43=21*2+1 47=23*2+1 51=25*2+1 53=26*2+1
And combined Prime Generalization: (Musatov)
RULE: Every prime greater than two is 1/2 a number +1 and twice a number +1.
Now consider the series again, but this time plot the additive difference between first and next doubled number.
In the first two terms we write.... 3=1*2+1 # 5=2*2+1 1 because the difference between the doubled numbers from first to the next was "1".
And we continue.... (here is the full table) 3=1*2+1 # 5=2*2+1 1 7=3*2+1 1 11=5*2+1 2 13=6*2+1 1 17=8*2+1 2 19=9*2+1 1 23=11*2+1 2 29=14*2+1 3 31=15*2+1 1 37=18*2+1 3 41=20*2+1 2 43=21*2+1 1 47=23*2+1 2 51=25*2+1 2 53=26*2+1 1
I would like to see if these reveals more to clarity to the set of primes.
How might it? Ben Bacarisse wrote: > Musatov <marty.musatov@gmail.com> writes: > > On Jun 20, 12:13 am, William Elliot <ma...@rdrop.remove.com> wrote: > <snip> > >> Exercise. How many primes are half of some prime plus one? > > > > None. Half of a prime number is not a whole number. > > Except for 2. > > > So we have the result: > > > > RULE: No prime number is 1/2 another prime number plus one. (Except for ) > > Just one prime number is exactly one plus 1/2 another prime number.
Oh yeah, which one?
> Copout per Ben.: Wording changed to avoid the ambiguity between p/2 + 1 and (p + 1)/2.) ++ Martin

