User talk:Dyablon2

See my user page. Post comments here. --- The YJ (Yablon-Jinydu) Conjecture is:

lim (n->infinity) Mn ^ (1/n) == 1.5000 == 3/2 == M2/M1,

where Mn is the nth Mersenne Prime,

i.e. M1==2, M2==3, M3==5, M4==7, M5==13, M6==17, M7==19, M8==31, M9==61, M10==89, etc.

This was discovered empirically by Yablon using a simple C-program to take nth roots of the first forty known Mersenne Primes. The approach to the limit of exactly 1.5000 == 3/2 was unmistakeable and is easily reproduceable.

With a proof of this conjecture, it is then easy to prove the Infinitude of the Mersenne Primes:

There are an infinite number of Mersenne Primes !!!!!

This is no longer an open question.

The YJ Conjecture is proven as follows:

(1) Prove lower and upper bounds on a constant K with sqrt2 < 1.47 < 2^gamma < K < 2^gamma*ln3 < lg3 < phi < sqrt3 < 2

such that the conjecture holds for limit == K if   there is any such limit.

(2) Prove K == 3/2 == 1.5000 using an epsilon-delta simple calculus proof.

This proves the above assertions.

(D.Yablon,2006-05-24)

Apologies. The conjecture has NOT been proven. 2007-01-29