p = +/- 3^x +/- 2^y
in [Math]
|
Prev: x^3+y^3+z^3 = N
Next: Mathematical Convention
From: The Pumpster on 20 Apr 2010 11:41 On Apr 20, 3:53 am, master1729 <tommy1...(a)gmail.com> wrote: > M.A.Fajjall wrote : > > > Is there any proof that any prime number can be > > expressed in the form > > p = +/- 3^x +/- 2^y > > > where x and y are positive integers > > that is incorrect. > > large enough p = 3^a + 3^b - 2^c - 2^d - 2^e - 2^f +/- O(14) > > tommy1729 I'm not sure what you mean by O(14) in this context. If you wish to claim that there exists some absolute constant k such that every "large" prime is the sum or difference of at most k powers of 2 and 3, this is simply not true.... de P
From: Gerry Myerson on 20 Apr 2010 18:42 In article <f1e7ed05-d89b-46d0-9521-a9c449b59b1b(a)l24g2000vbn.googlegroups.com>, Pubkeybreaker <pubkeybreaker(a)aol.com> wrote: > On Apr 20, 8:13�am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > On Apr 20, 5:28�am, "M.A.Fajjal" <h2...(a)yahoo.com> wrote: > > > > > > > > > > Is there any proof that any prime number can be > > > > expressed in the form > > > > � p = +/- 3^x +/- 2^y > > > > > > where x and y are positive integers > > > > > where x and y are non-negative integers- Hide quoted text - > > Count the number of integers of the form +/- 3^x +/- 2^y up to N. > Count the number of primes. > > Now let N --> oo. May not be so easy to count the numbers of, say, the form 3^x - 2^y up to N since some very large x and y could result in some relatively small N. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
From: The Pumpster on 20 Apr 2010 18:46 On Apr 20, 3:42 pm, Gerry Myerson <ge...(a)maths.mq.edi.ai.i2u4email> wrote: > In article > <f1e7ed05-d89b-46d0-9521-a9c449b59...(a)l24g2000vbn.googlegroups.com>, > > > > > > Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > On Apr 20, 8:13 am, Pubkeybreaker <pubkeybrea...(a)aol.com> wrote: > > > On Apr 20, 5:28 am, "M.A.Fajjal" <h2...(a)yahoo.com> wrote: > > > > > > Is there any proof that any prime number can be > > > > > expressed in the form > > > > > p = +/- 3^x +/- 2^y > > > > > > where x and y are positive integers > > > > > where x and y are non-negative integers- Hide quoted text - > > > Count the number of integers of the form +/- 3^x +/- 2^y up to N. > > Count the number of primes. > > > Now let N --> oo. > > May not be so easy to count the numbers of, say, the form > 3^x - 2^y up to N since some very large x and y could result > in some relatively small N. > > -- > Gerry Myerson (ge...(a)maths.mq.edi.ai) (i -> u for email) One can use |3^x-2^y| > 2^y/(y^k), valid for suitably large absolute k (this follows from lower bounds form linear forms in logs and was first proved, I think, by Tijdeman). de P
From: master1729 on 22 Apr 2010 04:29
Pumpledumplekins wrote : > On Apr 20, 3:53 am, master1729 <tommy1...(a)gmail.com> > wrote: > > M.A.Fajjall wrote : > > > > > Is there any proof that any prime number can be > > > expressed in the form > > > p = +/- 3^x +/- 2^y > > > > > where x and y are positive integers > > > > that is incorrect. > > > > large enough p = 3^a + 3^b - 2^c - 2^d - 2^e - 2^f > +/- O(14) > > > > tommy1729 > > I'm not sure what you mean by O(14) in this context. > If you wish > to claim that there exists some absolute constant k > such that > every "large" prime is the sum or difference of at > most k > powers of 2 and 3, this is simply not true.... > > de P Proof ? by O(14) i mean that the equation holds with precision 14. thus (lhs - rhs)^2 =< 14. although i ask for i proof , i already see you might be correct. by modular arithmetic mod some p , not all residues can be of the form 3^a + 3^b - 2^c - 2^d - 2^e - 2^f. and thus some primes are not of the form 3^a + 3^b - 2^c - 2^d - 2^e - 2^f. something like that i guess. is that equivalant to your intended disproof ? your a very good poster , i wish we had more like you on sci.math. sorry for the mistake , i was too impulsive. regards tommy1729 |