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very good chris and Luhn

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  • sta staf
    very good chris and Luhn yes : a²-b²= (a-b)(a+b) and if n is prime then a = n b = 1 i propse to formalize this theorem in thes legendre s conjecture .
    Message 1 of 3 , Jun 16, 2009
      very good chris and Luhn



      yes :



      a²-b²= (a-b)(a+b)





      and



      if n is prime then a = n

      b = 1



      i propse to formalize this theorem in thes legendre's conjecture .





      a²-b² = (a-b)(a+b)





      ab = ((a+b)/2)² - ((a-b)/2)²





      n*1 = ((n+1)/2)² - ((n-1)/2)²





      = 1*n === the Legendre's conjecture, there is a prime number between n² and (n + 1)² for every positive integer .



      To: primenumbers@yahoogroups.com
      From: caldwell@...
      Date: Mon, 15 Jun 2009 20:46:20 -0500
      Subject: RE: [PrimeNumbers] RE: Yahoo! Groups: Welcome to primenumbers. Visit today!










      A^2 - B^2 = (A-B)(A+B)

      So you conjecture is similar to the claim that 4n is never prime
      for positive integers n. True, but empty.

      Chris.

      -----Original Message-----
      From: primenumbers@yahoogroups.com [mailto:primenumbers@yahoogroups.com] On Behalf Of sta staf
      Sent: Monday, June 15, 2009 8:42 PM
      To: primenumbers@yahoogroups.com
      Subject: [PrimeNumbers] RE: Yahoo! Groups: Welcome to primenumbers. Visit today!

      CONJECTURE:
      there is no prime of the form A² - B²
      where A, B are positive integers and A-B >1 .

      Questions:
      give me a counterexample .

      finding a counterxample - has a cash prize of $ 1000 USD.


      Thanks

      RACHID BAIH

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