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Topic: 2nd proof that Infinity border is Floor-pi*10^603 via even
divisibility #1571 Correcting Math

Replies: 4   Last Post: Feb 23, 2014 2:00 PM

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 plutonium.archimedes@gmail.com Posts: 8,734 Registered: 3/31/08
2nd proof that Infinity border is Floor-pi*10^603 via even
divisibility #1571 Correcting Math

Posted: Feb 20, 2014 3:12 AM

2nd proof that Infinity border is Floor-pi*10^603 via even divisibility #1571 Correcting Math

It is no secret that I am looking for an alternate proof that the number Floor-pi*10^603 is the border between finite and infinite. I proved this via unit Tractrix area crosses over that of the unit Circle area for the first time at this number, hence the border of infinity.

Now I want a different proof that does not use area analysis. A proof that uses purely "even divisibility". We know pi is evenly divisible by 2 by 3 by 4 and by 5 in order to have the regular polyhedra and regular polygons. So our borderline of Infinity has to satisfy that even divisible by 5! = 120.

Now at the digits of pi of its 601, and 602 and 603 digits rightward of the decimal point 3.14159..132000 that pi is evenly divisible by 120 at 601, and 602 and 603.

But, let us ask a fun question, or question for fun. Let us take 120 times 120 times 120 and we get 1728000 with three zero digits at the end. Now, let us keep multiplying that number by numbers which are never 5 since a 5 would tack on more zeroes at the end, but we want only three zeroes always at the end. And let us multiply that number to try to achieve in the end 604 digits altogether the first few being 3145 and the last six being 132000.

In other words, in this game of fun, we start with the number 120^3 and we apply multiplication to see how close we can come to Floor-pi*10^603.

Now, I think I can come awfully close to Floor-pi. But I would be astounded to think I can achieve Floor-pi exactly.

So here are a few routes to take:

7 times 120^3 = 12096000
3 times prior = 36288000

Let me try a different cascade:

3 times 120^3 = 5184000
2 times prior = 10368000
3 times prior = 31104000

So with only three multiplications so far I achieved a 311.. which is close to a 314..

Now I do not know if the best result will be to limit the multipliers to just 2,3,4,6,7,8,9 or to allow higher multipliers, but none which would increase the end trailing three zeroes.

So, how close can this fun exercise get me to actual Floor-pi*10^603? Can it deliver to me exact Floor pi? If it can then this would be a proof of the Infinity border.

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