valid Indirect Euclid IP leads to twin prime proof #4.12 Correcting Math
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From: Archimedes Plutonium on 24 Jul 2010 02:15 Transfer Principle wrote: > On Jul 23, 1:00 pm, Archimedes Plutonium (snipped) This is not quite being fair to me Lwalk. I deliver an entire proof, one which can be published in a book. I deliver both Direct and Indirect in long form and in short form: short form Indirect (1) definition of prime number (2) hypothetical assumption, assume the primes are finite and that the sequence list is 2,3, 5, 7, 11, . . , p_k (3) multiply the lot and add 1, calling it W+1 (4) W+1 is necessarily a new prime because of definition in (1) joining with the fact that division of W+1 by all the primes that exist in (2) leave a remainder (5) contradiction to (2) that p_k is the largest and last prime, for W +1 is now the largest prime (6) reverse supposition step (2) and primes are infinite Not fair to me to compare mine with someone who never writes out a proof, never a step by step. Always jumps in, in midair with hatemongering. I do not deserve to be compared with someone who is unable to write out a proof. LWalk, every Euclid IP Indirect must start off with the definition of prime, for we all must know what we are talking about as step 1. And the definition is critical in both methods when we inspect W+1. Most authors of Euclid attempts, most every auther, even Ore omits the definiton, and technically every proof that omits the definition in step one is invalid, but that is a minor invalidity. The major invalidity in the Indirect is not realizing that W+1 is necessarily a prime number. Step 1 ---- definition Step 2 ---- assume all existing primes with p_k the last and largest Step 3 ---- form W+1 All Indirect Euclid IP must have those three elements, and forces a unique proof. It is because you have this Euclid Number of multiply the lot, which is divisable by all the primes of that finite set, but because you added 1, none of the primes of the finite set divides. So W+1 is necessarily prime. Now you look back to step 1, and you are forced by the definition to say W+1 is necessarily a new prime. Definition plus p_k the largest prime plus the forming of W+1, makes Euclid Indirect a unique proof of its steps. Sure, some hatemonger can tack on extraneous garbage steps; can waffle about units or waffle about composites. But all valid Euclid Indirect boil down to a unique chain of events. Definition plus p_k plus W+1 forces W+1 as a necessarily new prime and thus the proof. And because no-one really had a valid Euclid IP Indirect until the 1990s, that no-one in all of mathematics was ever going to prove infinitude of twin primes, because the only route to a proof of twin primes was via the Euclid Indirect. > And so which side do I believe is right? Answer: _both_ are right! > You say this only because you are too nice of a guy that does not want to hurt the feelings of a hatemonger. But I do not think you should compromise math or a science, just to be nice to another person. I think truth trumps being nice. Question LWalk: is there something in Galois algebra that says the Twin Primes are a subset of the Regular Primes, and since we have an infinitude proof both direct and indirect, is there something in Galois Algebra that says the Indirect or Direct must also be the basis of a proof of twin primes infinitude? I believe there is, but just do not know the technical term for this. The idea here is that if a proof of a larger set is found, then that proof must be able to wrangle out a proof for the subset. So in other words, the twin primes proof needed only the fixing of the invalid proof attempts of the past in order to provide a simple easy twin primes proof. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |