Recent content by geraldmcgarvey

Here's a little more regarding Matt Grime's proof: "let x = 10q+r, where 0<=r<9 x^2 = 100q^2+20rq + r^2" and as he noted, r must be 1 or 9 If it is 1 there is no carry, so the ten's value will be 2rq, which is even and not 1. If it is 9 then r^2 = 81, so carry the 8. But then 8 +...

something to note, 17 and 886731088897 are both in the sequence described at this link: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A001541 specifically they are at offsets 2 and 16 respectively.

I don't have a proof, but maybe this link can help if you haven't seen it already: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A000215 Are you trying to prove that only the first 5 numbers in this sequence are prime? If you can, it's certainly worth doing.

Think in terms of multiplication. "Zurtex, 5^10 = 5+5+5+5+5+5+5+5+5+5 Similarly, what is 0.5^10? I want an answer in terms of addition (or subtraction maybe)" 5^10 is not 5+5+5+5+5+5+5+5+5+5 (which is 5*10), 5^10 is 5*5*5*5*5*5*5*5*5*5 similarly, .5 is .5*.5*.5*.5*.5*.5*.5*.5*.5*.5 which...

1. sqrt(2), sqrt(3), sqrt(5) 2. Apery's constant i.e. zeta(3), and zeta(2) 3. Khinchin-Levy constants 4. Madelung's constant (related to 3D NaCl crystal)

A circle is not a physical object. "if you measured all the way down to the very last atom" A circle is not a physical object that can be measured, it is a mathematical object. There's a distinct difference between mathematics, which is used to model the physical world, and the physical...

Randomness can be defined in different ways. From the perspective of data processing it can mean incompressible by an algorithm of shorter length than the data. So are the digits of Pi random? In one sense they are, but if you know the trick they aren't. Then there is statistical randomness...

I don't think so. How can qualitative experiences (qualia), such as the experience of colors, emotions, tones, etc. be described quantitatively? Maybe they can be correlated to triggers that can be described quantitatively, but that is different than actually describing them. We can...

Quote from Albert Einstein It is best to cut down on consumption of animal foods, particularly from factory farms. There are several benefits. Protecting our environment: . It takes much less resources and causes less pollution to produce plant food. . Factory farms pollute our environment...

p*p "A multiple between two primes is always right in the middle of two primes." Has that been proven, that the product of two primes is always the average of two primes? Are all numbers > 2 the average of two primes?

Here's a little more on 'negabinary' which was used by experimental Polish computers in 1950: http://encyclopedia.thefreedictionary.com/Negabinary http://mathworld.wolfram.com/Negabinary.html also negadecimal: http://mathworld.wolfram.com/Negadecimal.html It looks like negative bases are...

For a good - and inexpensive - introduction to partitions, you can consider the book 'Number Theory' by George E. Andrews, who is an expert, a reviewer at Amazon says 'the reigning expert'.

Nonstandard Analysis This thread touches upon nonstandard analysis, see http://mathworld.wolfram.com/NonstandardAnalysis.html http://mathworld.wolfram.com/HyperrealNumber.html As to a smallest positive real number, there isn't one, infinitesimal numbers are not real numbers. My limited...

Negative bases Interesting concept, here's some links to info on negative bases: http://mathforum.org/library/drmath/view/55710.html http://www.maa.org/devlin/devlinfeb.html One thing the articles point out is that no sign is necessary, instead negative and positive numbers differ in their...

Mertens function See http://mathworld.wolfram.com/MertensFunction.html Sum n=1..x M(x/n) = 1 (Lehman 1960) [How do you get the graphic version, do you submit it in Latex format and this website does the rest?]