## Recent discoveries

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• Hello, While I ve been offline, I ve been working hard at some new ideas in twin prime theory, which I hope to share here (mostly trying to come up with a
Message 1 of 1 , Feb 2, 2002
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Hello,

While I've been offline, I've been working hard at some new ideas in
twin prime theory, which I hope to share here (mostly trying to come
up with a Chebyshev analogy to twins ie theta_2(x)=O(x) and things
like that.)

Let M(n)=log p if n=p^k, k>=1, zero otherwise (von Mangoldt function)

then sum (2<n<=x, condition M(n)*M(n+2)>zero) M(n)/n =2*c*loglog x +
M + O(1), where M =Merten's constant, and c is the twin prime
constant.

Can this be proven by combining sum (primes<=x) 1/p ~ loglog x with
the Hardy-Littlewood theory, and R Padma's double mangoldt function
(which is sum (n<=x) M(n)*M(n+d), where d is even, and I've only used
d=2)?

That'll do for now. I'll post another sometime soon,
from Guy
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