If you have been following our Tablet coverage, you must know how hot the market is and the temperature is just going to rise in coming months. Many many big companies are gearing up with their Android and Windows 7 based tablets, to give a fight to iPad which is clearing ruling the tablet space right now. Latest to join the race is Toshiba, although it is already having a dual screen tablet in the market, but this will their first in the iPad form factor devices. The table is called Smartpad and as per reports from notebookitalia itRead More
“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate“. Leonhard Euler in George Simmons, Calculus Gems, 1992
Most statements in number theory, as in mathematics as a whole, are concerned with a whole class of numbers (like class of even numbers or class of squares of integers… etc). The fundamental importance in number theory is the class of all ‘Primes’. A prime is an integer p, greater than one, which has no factors other than itself and one. An integer (other than 0 and 1) which is not prime is said to be Composite. For example, 5 is always a prime whether it is written as 5 or as the binary form 101 or in any other system of numeration. The largest known prime as of 2005 has 7,816,230 digits. The numeral 2 is the only even prime number.
One of the first question that arise concerning the class of prime is that whether there are only a finite number of primes or infinitely many members?
Proof: This most elegant proof was given by Euclid circa 300BC. We begin by assuming that the number of primes is finite. Let us denote them by p1, p2… pn, so that p1 = 2, p2 = 3, p3 = 5, and so on. Now consider the number
q = p1*p2*p3* ···*pn + 1, ——— (1)
where we have multiplied together all the primes, and added with one. This integer ‘q’ cannot be a prime. Since it is larger than all n primes and ‘q’ must have a prime factor, say p, which must be one of the primes p1, p2. . . pn. But it is clear from (1) that none of these primes divides q. This contradicts the initial assumption that was made ion the beginning that the number of primes is finite. Hence it is concluded that the number of primes is infinite.
The importance to the class of primes is due to the fact that every integer can be expressed as a Product of Primes. Any integer N greater than 1 can be factored into a product of primes n only one way. Every positive integer n can be written uniquely in the form
n = p1a1. p2a2. p3a3… pNaN.
For some choice of N, where
p1 = 2, p2 = 3, p3 = 5,… are the prime numbers. Each exponent a1, a2, a3,…aN. a1 is a nonnegative Read More
After the much successful HTC Desire, the company is getting ready to come up with upgraded version of the smartphone. The UK mobile retailer mobiles.co.uk leaked some info about the upcoming devices. There will 2 devices launched in total to carry on the HTC Desire line and will be called Desire Z & HD. Some HTC Desire Z Specification details : 1. 3.7 inch capacitive touchscreen display 2. Will support an impressive 480x800 resolution 3. Will be powered by 1 GHz Qualcomm's Snapdragon microprocessor. 4. Slide out Qwerty keyboard 5. Will apparently run on Android 2.1(hope it doesn't) 6. Upto 32GB microSD memory support. Some HTC DesireRead More
Google is testing a new feature that will display search results as you types your search text/ query without hitting any key stroke, yeah no 'Enter' or ' Return' required. This works when you start typing in the search box located on top of the site (unlike the traditional page where the search box is in middle of screen) results are changed to match whatever you enter in the text box These live search results are not available to the public at large. Google regularly tests new features with very small selections of users. Some of those features neverRead More
Here is a comedy spoof which shows you how exposing your facebook profile to millions of people worldwide might affect your job prospects. I do get the pun intended and its hard to find a profile like the guy in the video but still do keep a note, facebook profiles can be part of background checks in future :) . via: wiseguypictures
If you think your table is too heavy and its a nightmarish to move it around, than The Walking Table is the one solution you are looking for. via
Already The Social Network, the story of Facebook and its founder Mark Zuckerberg is schedule to hit theaters in October, now a story has appeared that there will be a movie on Google and its founders, Segrey Brin and Larry Page. Deadline is reporting that Michael London’s Groundswell Productions and producer John Morris have together purchased the movie rights for Googled: The End of the World As We Know it. The 400-page Google narrative, published in late 2009, was authored by The New Yorker columnist Ken Auletta. “The heart of the movie is their wonderful edict, don’t be evil. At aRead More
If you are looking for a dual screen tablet which actually exists in the market and is not a vaporware than Toshiba Libretto W100 is the one for you. We did cover the tablet when it was announced in the post here and was mentioned that it will be available in August 2010 with a price tag of around $1100. And it did happen, the impressive tablet was available on Amazon(Link) for a brief time before being marked as out of stock. Its hard to imagine how many devices were sold to bring to the out of stock situation orRead More
What Twitter has released a browser-based tweet button that provides a simple way for Twitter users to click to share the web page they’re on with followers. Twitter users can drag the “Share on Twitter” bookmarket to their browser’s bookmarks bar — all major browsers are supported. The Share Bookmarklet makes it easy for you to share any webpage on Twitter, even if there isn’t a Tweet Button. It works in all major browsers and is easy to install. How To use the bookmarklet just drag the Share on Twitter button to your Bookmarks Bar, browse for a page your like and thenRead More
According to an open letter posted on Like.com’s website Google has acquired visual search and price comparison engine Like.com. “Since 2006, Like.com has been moving the frontiers of eCommerce forward one step at a time,” said Munjal Shah, the company’s CEO. “We were the first to bring visual search to shopping, the first to build an automated cross-matching system for clothing, and more. We didn’t stop there, and we don’t have plans to stop now. We see joining Google as a way to supersize our vision and supercharge our passion.” About Like.com - Launched in 2006 a facial recognition search engineRead More