The countdown
Hi there ! Koavolt's not in right now. This is jtox making a guest post on Koavolt's page. Just thought I'd let you all know that he's doing fine... just getting over a serious cold, still working on the uber-oldschool volkswagon bug of salty metallic goodness. There's oh so much more to tell about his current life, but it just wouldn't be right for me to post it all without his consent ... *evil grin* ... at least, it wouldn't if I didn't give him a sporting chance to make his own post ;-) .

Time is your friend, but when neglected, it tends to get hasty and impatient.


And now for my long-awaited Super-Off-Topic Post Attack!


As a side note: yes, it IS possible to show that there will always be at least one prime between n² and (n+1)² (and even maybe (n²,(n²+n))) via using solid 2D squares that show there will always be at least one remainder less than 2n+1 that when added to n², gives a prime number, which needs help from group theory - and maybe, more specifically, dealing with spiral variants and circles via group theory. But has anyone done it yet? Nope. The problem lies in that it's trivially easy to prove that the converse is true. (Given a prime p, there is always an integer n such that n² <>2) And in fact, looking at this converse, wouldn't it be easy to prove via induction if we had a function available that gives us the next prime P_next ? In fact, there are such functions - ranging from actual algorithms, huge equations and formulas, unfortunately they are all quite dauntingly unweildly for this task, the king of which is proving the Riemann Hypothesis (which would teach us fascinating relationships not just with prime numbers, but with an infinite range of number sequences and their variants) ... It certainly doesn't eliminate the possibility of using the actual functions that we do have in place ... but it would take a lot of brilliance, math experience (at least twice the comfort level that I'm at with mathematics), and finally, free time and/or paid hours to do so; most people have neither unless they are university professors. So for those of you as constantly hounded by these mysteries and puzzles as I am, I feel your anguish, and join your ranks at the very sidelines of the field of mathematics in eager anticipation of the new discoveries and accomplishments made by the top players and underdogs, knowing that just maybe, we could be out there, too.
- posted by James @ 7:09 PM

 
To fubar, or not to fubar ... that is the question.
Stay tuned.
- posted by James @ 9:49 PM