## very good chris and Luhn

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• 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 .

From: caldwell@...
Date: Mon, 15 Jun 2009 20:46:20 -0500

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-----
Sent: Monday, June 15, 2009 8:42 PM

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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