Do you think order will finally be found in the seemingly chaotic and random nature of prime numbers? Or is the obsession to find order just a constraint of human thinking?
The RSA security foundation is built on prime numbers. We're using primes in our E commerce/banking security but really haven't cracked the code so to speak.
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The 18th - 29th digits of the true safe withdrawal rate is a very long prime! :
__________________ Often uninformed, seldom undecided.
Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain
I find the Fibonacci Numbers and The Golden Ratio more fascinating myself, due to it's almost ubiquitous presence in nature. Sea Shells, Flower Petals, Pine Cones, Plant Stems all follow this sequence, and paintings and architecture seem most pleasing to the eye when using this ratio. Neat stuff.
Chaos Theory is neat, though. I don't personally believe the obsession to find order is a constraint of human thinking. After all, we keep finding it! The thing is, since the big bang, the universe has gone from perfect order to more and more chaos, entropy continues to do it's work as the universe expands. Life is like a little, defiant shout against disorder, reversing entropy a tiny bit for just a blink of time. I think I heard somewhere that eventually matter and energy will dissapate over such a broad area that all the stars with snuff out and there won't be enough matter in any one place to form new ones. A Dark Universe, where only dust and low levels of infrared energy scuttle across an impossibly empty chasm of space. That would kind of suck. Maybe at some point the universe will contract again and we start the process all over?
__________________ "off with their heads"~~dr. joseph-ignace guillotin
"life should begin with age and its privileges and accumulations, and end with youth and its capacity to splendidly enjoy such advantages."~~mark twain - letter to edward kimmitt 1901
Theorem.
There are more primes than found in any finite list of primes.
Proof.
Call the primes in our finite list p1, p2, ..., pr. Let P be any common multiple of these primes plus one (for example, P = p1p2...pr+1). Now P is either prime or it is not. If it is prime, then P is a prime that was not in our list. If P is not prime, then it is divisible by some prime, call it p. Notice p can not be any of p1, p2, ..., pr, otherwise p would divide 1, which is impossible. So this prime p is some prime that was not in our original list. Either way, the original list was incomplete.
I find Cantor's logical reasoning about infinite quantities to be more interesting than prime numbers.* The revelation that there is an unbounded hierarchy of infinities remains astounding.* David Hilbert, the "King" of mathematics 100 years ago, said
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"No one shall expel us from the Paradise that Cantor has created."
if you're really fascinated you might find the following site of interest: "an exciting collection of curiosities, wonders and trivia related to prime numbers" (i'm not fascinated, but did find this of interest nonetheless) http://primes.utm.edu/curios/
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Linear Mode
