wow!!! I wonder if we have a Ramanujan Jr. in our midst
excellent work Don!!
my first impression mental inclinations on this discovery are similar to Craig's.. namely that the need for so many accurate decimal places will detract some from its practical applications.. but the over-arching excitement of this is still intact and palpable IMO...
IMO it would be like finding a triple relationship between Planck's Constant, PI, and who knows what else... Making such a discovery I would feel like I was at the entrance to a labyrinth of unknown depth, and be intensely wondering what goodies are at its center and various side rooms. And whether any indwelling minotaurs were open to bribery.
Should it hold up to the ultimate scrutiny of your peers, I hope you are financially rewarded in some way, in addition to other deserved accolades.
Applying it to the Mersenne challenge might indeed be one road to cash, but then again if the test of primality involves searching for every possible composite pair... not sure how that would fit in.. or trump the Lucas–Lehmer test in speed... oh well in any case good luck sir, may the cash make its way into your bank acct with all due haste hahaha!
oh hey! idea! well on second thought this may be very trivial and obvious... but gonna mention it just in case this has some relevance or research value:
I wonder if the GIMPS team and other Mersenne researchers have numbered their primes... one of the very nice properties of your method is that X tells you which prime in the infinite sequence it is... and from what I understand the Mersenne research proceeds as a huge leapfrog, from one primal vista to the next as (2^n-1)'s n is each time bumped to a higher prime... I would presume that by doing so they are leaping over hundreds if not thousands of interval plain-jane primes that lie between the Mersenne milestones, if you will, and thus have no freakin idea what sequence # their primes have.
and since your method has the very nice property of knowing what X you are at... i wonder if there is a relationship just waiting to be unearthed in how the X proceeds from Mersenne to Mersenne... like just for example.... gonna throw out some random numbers that for sure do not correspond to reality but just to make the point... say Mersenne Prime #43 has an X of 111 and say that MP #44 has an X of 222 and MP #45 has an X of 333... always this bumping of X by 111.. that might be a cool track to search for patterns on.... but then again if the test for Mersenne primality somehow authoritatively goes through all the smaller numbers that would imply there is a pretty strong chance that they do already know what X they are at... hmm... but if Lucas-Lehmer is strongly oriented for speed and weakly oriented for authority, like I suspect it is, that leaves a door open for somebody to leap thru yay... and even if these science teams do know every sequence #... it still remains possible that nobody amongst them has bothered to search for any occult properties or patterns in their values.
well i'll stop babbling lol.. not sure if i'm making sense haha... gonna first look into the matter of if the sequence numbers have already been established or not.
