
Re: Musatov Prime Generalization Conjecture
Posted:
Jun 30, 2009 2:49 AM


*Musatov: Alf P. Steinbach wrote: > * Musatov: > > > > "Musatov's Prime Generalization Conjecture": Every prime greater than > > 2 is 2n+1=P. > > > > 2*1+1=3 > > 2*2+1=5 > > ... > > 2*20+1=41 > > ... > > > > (1)Is my conjecture provable? > > Yes but it's completely silly to conjecture that primes greater than 2 are odd. > > > Cheers & hth., > >  Alf > >  > Due to hosting requirements I need visits to <url: http://alfps.izfree.com/>. > No ads, and there is some C++ stuff! :) Just going there is good. Linking > to it is even better! Thanks in advance!
Dear Alf,
Thanks for the reply. I figure I have to start somewhere, thanks for bearing with me.
(1)So have we established every prime greater than 2 is 2N+1?
(2)Also, "2N+1"="odd", correct?
To quote (play on) the movie "Pi":
Musatov: "11:31pm. Restate my assumptions".
1. Every prime is odd.
2. "2N+1" is every prime greater than 2.
3. "2N+1" is every odd.
4. 2N+1 contains every prime greater than 2 plus every odd composite.
5. All prime factors of odd composites are contained in "2N+1".
6. The set of prime numbers and prime factors of of odd composites is wholly contained in the set "2N+1".
.......Breather........
The next step is then to establish the case when "N" is even, in every case "2N+1" is odd. If all of "2N+1" is odd then this is a given.
Now we further examine the states:
When "N" ends in "2":
2*2=4+1=5 is prime, but only the first time. Every number ending in 5 greater than 5 is composite.
So to generate primes by this method we can rule out all numbers ending in "2".
Then,
N of all even numbers we can say, there only remains numbers ending in "4, 6, and 8".
Consider each case:
For four: (#4)
2*4+1=9 not prime 2*14+1=29 prime 2*24+1=49 not prime
In the above instances "N" ends in "4" and is not prime, the formula produces a number with square prime factors (i.e. 3*3=9 and 7*7=49). (i.e. When it does not produce a prime the composite is a prime squared).
Also, we note:
When "N" ends in "4" and the formula produces a composite number, adding "two" to the composite produces a prime.
Shown: 2*4+1=9+2=11 prime 2*24+1=49+2=51 prime
Moving along...
For Six: (i.e. When "N" ends in "6" and is applied 2N+1)
2*6=12+1=13 prime 2*16=32+1=33 is not prime. 2*26=52+1=53 prime
As above when "N" ends in 6 and does not produce prime (as above) we have two prime factors.
In the above case of 33 they are "3 and 11". Of those two prime factors, adding 2 to each produces 2 more primes. Shown:
3+2=5 prime 11+2=13 prime
Now, onto 8: 2*8+1=17 prime 2*18+1=37 prime 2*28+1=57 prime 2*38+1=77 not prime
In the above we have when "N" ends in "8" and does not produce a prime as applied (2N+1) it has produced a number with two prime factors:
77=11*7
11 and 7 are prime.
Also, 11+2 is prime.
However, 7+4 is prime.
The conjecture contains:
"Musatov Prime Generalization Conjecture": "Every prime number and prime factors of odd composites, is contained in the set 2N+1."
The natural further question is how and when do prime factors appear in even composites and what rules apply?
So we have separated the primes and prime factors of odd composites into a set (2N+1), now the only remaining prime factors exist inside even composites and outside of this set.
A lot to chew on, but I thank you all in advance and look forward to the insight gained from your responses.
Signed,
++ Musatov

