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Anderson's Theorem (a) The number of primes in [1,n] is no more than 2+floor(n/2). The probability of n being prime when n is not prime is 1/2 - see Dasgupta,Papadimitriou,Vazirani "Algorithms" page 26. Therefore, the E(pi(n)) is n/2. (b) There does not exist another set of adjacent primes other than {1,2,3} 5: 2 + floor(5/2) = 2 + 2 = 4:=> {1,2,3,5} : 4 <= 4 26: 2 + floor(26/2) = 15 => {1,2,3,5,7,11,13,17,19,23} : 10 <= 15 Langrage's Theorem is Wrong Langrange's theorem about primes states that pi(x) is the number of primes <= x. The pi(x) is approximately x/ln(x). He postulated that the lim of pi(x)/(x/lnx) as x-> infinity was 1. This is incorrect. if the number of primes is bounded by n/2 then refactoring and reducing Lagrange's Theorem results in the lim of ln(x) as x approaches infinity. This is always infinity. Lagrange's theorem on some tests: 5: 5 / ln(5) = 3.1, incorrect 26: 7.9, incorrect

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Computer scientists like to talk about the number of atoms in the universe when talking about computational complexity. If you have 10**100 nodes to evaluate, and there are only 10**86 atoms in the universe, then there is no way to compute your node tree. 10**86 atoms? Where does that number come from? Who made this up. In [1] the claim is that there are 10**86 hydrogen atoms out there. That seems like alot, right? Remember Avogadro? He came up with a number too [2]. His number is 6.022 x 10**23 atoms per mole. That's alot of atoms too, right? Hmm. If you had one cubic mole of something, how many atoms are in there? Well, that's (10**23)**3, or about 10**69. That's not 10**86, but it's close. How many cubic moles are 10**86 atoms then? Well, about 86/69, or about 1.25 cubic moles. So the total sum of all atoms in the universe is just 1.25 cubic moles? Or rather, let's topsy turvy this. There are more atoms in 1.3 cubic moles of water than the universe. Ah

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It's time for HTML of the future to give us the ability to obfuscate data in-memory. If password fields were stored as obfuscated values, then there would be a very low chance of a password recovery by any person or any exemplary skill. Plus, we wouldn't have to rely upon client-side JS to do hash obfuscation. I suggest a simple extension to the input form element: [ input type='password' obfuscator='sha512;salt=FooFooFoo' ] We would define our own salt, or no salt, to keep the hash consistent (homomorphic) across creation and challenge. This can be done with JS but it doesn't prevent malicious adware JS from exploring the DOM and getting the "value()" property of an input element that is named "password". Pretty please?

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Today I got a phishing email for my gatech account. It was nothing special and easy to identify as phishing. So why blog about it? Because today I decided to test out safelinks. Why not, right? It's Microsoft, and they make a habit of telling me that I should use Edge because it is safer than Chrome and Firefox. I clicked on the safelink that was hosted on eur03.safelinks.protection.outlook.com and it opened in Edge. Wait, why did I have to hit a European safelink server Microsoft, if I am in the USA? I don't remember authorizing you to do that, but then again, who cares about us in the US. The safelink redirected successfully to logins.gatech.com which is a shameless phishing site. It pulls resources from gatech.edu but has a self hosted JS file that has the same URL path as the one in the buzzport login page. It's a clever phish and it would likely defeat most users. So that made me mad. I put on my Cyber cape and started to dig. The IP is hosted on AWS: Name:

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The HP site for buying stuff on their Labor Day Sale is broken. I tried it on other computers and each had the same result. Not sure if HP was able to sell anything on their big sale weekend, but I couldn't buy anything. Funny part was the feedback widget that didn't work. Not only could I not buy anything from HP but I couldn't report the problem I was having. Maybe someone at HP could run this through QA again.

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