Re: Hardy Littlewood Conjecture
- --- In firstname.lastname@example.org,
"ALBERTO" <arfzelaya@...> wrote:
> Let p any prime of the form 6k+-1...
> and n any integer number
> if an integer x is not equal to pn+-kLet's try to parse that carefully.
> it won't be equal to 6ab+-a+-b
(I failed to do so, previously, sorry.)
Proposition: Let x be a positive integer for which there exists
at least one triplet (a,b,s) with integers a >= b > 0
and a sign s = +/-1 such that x = 6*a*b + s*(a+b).
Then there exists at least one such triplet for which
at least one of 6*a + s and 6*b + s is prime.
Proof: 6*x + 1 = (6*a + s)*(6*b + s) has at least one prime divisor.
Example 1: With x = 1627604, there are 5 triplets,
yielding only 1 prime, since 6*x + 1 = 5^10.
Example 2: With x = 6197024, there are 63 triplets,
yielding 7 primes, since 6*x + 1 = 23#/6.
Question for Alberto: What has this to do with H+L ?
David (with apologies for earlier stupidity)