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Euclid’s theorem: Proof of Infinitely many primes

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Also known as the Euclid’s theorem, the theorem of infinitely many primes is one of the most elegant ones around. I came across it while brushing up on discrete math and had to blog about it. Let's try to explain a proof of this theorem. Before we begin, lets revisit the following things: Any number can be written as a product of prime numbers as stated in the fundamental theorem of arithmetic. The number sets   Here we go! To prove: There are infinite prime numbers Let’s dispute that claim for a second and assume that we know all the prime numbers. Let’s write these as follows: P 1 P 2 P 3 ….P n Lets try to form a new number Q the following way: Q = P 1 x P 2 x P 3 x   ….P n + 1 Now, Q can either be: Prime Non prime Why? Because any natural number > 1 has to be either prime or non prime. If its: Prime, our list was incomplete as there is at least...

Dynamic Programming Example

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Dynamic programming problem explained and solved using C++. I like programming in general, but the paradigm which appeals to me most is Dynamic programming. Back in 2013, during my college days, I used to  hone my skills by solving problems on CodeChef. But then I got a job and it does not involve a lot of DP. Recently I've realized that I have become clumsy, and too used to the "safe life", hence I've decided to solve DP problems on HackerEarth, the purpose of this blog is to keep me motivated :p Samu and Shopping Samu is in super market and in a mood to do a lot of shopping. She needs to buy shirts, pants and shoes for herself and her family. There are N different shops. Each shop contains all these three items but at different prices. Now Samu has a strategy that she won't buy the same item from the current shop if she had already bought that item from the shop adjacent to the current shop. Now Samu is confused, because although she want to foll...

SAP Labs India Interview Experience

This is regarding the selection process of SAP labs for the 2014 batch. The process was divided into two main parts 1: Online Test 2: Interviews Online Test  It had the following sections: Quantitative Aptitude  Basic Programming knowledge ( O.O concepts, Output prediction etc ) English Code ( Candidates had to write code for a problem statement ) Most candidates faced problems in the code section so I advice students to Practice writing code, preferably on Online code editors. Interviews Students who cleared the written round were called for Interviews. There were 4 interviews in total Two technical one Managerial and one Hr. The First Interview The first interviews is to check the basic knowledge of almost all core subjects such as Data Structures,Operating Systems, DBMS etc. O.O Concepts are of particular Importance Questions will be asked on the basics of programming language(s) Of candidate's choice,the candidates are also expected to wri...
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littleBits Goes a Long Way "The goal -- and challenge -- in this project was to create highly respectful, scientifically accurate projects that replicate NASA's groundbreaking work, while also making them modern, engaging and fun for nonscientists," said littleBits Product Designer Krystal Persaud. "We think this will empower people who were previously uninterested in STEM to get excited and get involved." Space fans the world over long have dreamed of exploring the universe for themselves, but a new, 12-module kit from NASA and  littleBits  aims to give enthusiasts a way to bring the thrill of space exploration closer to home. The new littleBits Space Kit, launched on Thursday, includes an assortment of electronic modules and NASA-designed projects and activities designed to allow anyone to observe and measure the universe, build and remotely control a model Mars Rover, or wirelessly send music to a model of the International Space Station. ...

Gmail - Undo Send

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You clicked send. Oh crap. When you send a no-take-backs email — maybe an official email, or accidental reply-all — there's an instant pang of regret. It feels like there's no going back. Meet Gmail's Undo Send feature, a lifesaving little hack buried in the Gmail Labs settings. It gives you a 30-second window to "undo" sending an outgoing email. You just have to enable it first. Here's how it works: 1. Click the gear icon in the top-right corner of your Gmail window and select Settings from the dropdown menu. Gmail screenshot 2. Select Labs from the row of tabs. Gmail screenshot 3. Scroll all the way to the bottom where you see Undo Send and click Enable. Gmail screenshot 4. Hit Save Changes at the bottom. 5. Breathe easy. Now when you send an email, the yellow dialogue that displays "Your message has been sent" will also give you the option to Undo. Click it, and the email will reop...

Google says next version of Android will be called KitKat

Google says next version of Android will be called KitKat NEW DELHI: Sundar Pichai, head of Android division at Google, on Tuesday revealed on Twitter that the next version of the company's mobile operating system (OS) will be called Android KitKat. "We now have over 1 billion Android activations and hope this guy in front of the building keeps that momentum going," Pichai tweeted as well as posted an image of a giant Android mascot built like KitKat chocolate. Earlier, there were rumours that the next version of the OS would be called Android Key Lime Pie. Since Android 1.5, Google has named each version of the OS after a sweet. Android 1.5 was Cupcake. Android 1.6 was Donut. Android 2.0 was Eclair. Android 2.2 was Froyo. Android 2.3 was Gingerbread. Android 3.0 was Honeycomb. Android 4.0 was Ice Cream Sandwich. And Android 4.1, 4.2 and 4.3 have been called Jelly Bean. "Android is the operating system that powers over 1 billion smartpho...

MICROSOFT NOKIA DEAL

Microsoft's Nokia deal: Layoffs look inevitable   ( read original ) BANGALORE: Microsoft and Nokia's India operations are among the biggest outside their home countries, and it looks like a certain number of redundancies and consequent layoffs are inevitable. Microsoft CEO Steve Ballmer's email to Microsoft employees on the Nokia deal said the companies would integrate all global marketing and have a unified brand and advertising strategy. It said that finance, legal, HR, communications, evangelism, customer care and business development would integrate functionally at Microsoft. ICM/IT will also integrate functionally for traditional IT roles, it said. Such integration in most cases implies redundancies. Nokia has 9,000 employees in India, almost a tenth of its global workforce. Microsoft has 6,000 employees here, out of its global strength of 97,000. It's unlikely that there will be much overlap at the engineering, support and R&D lev...

Why Russian Tech Entrepreneurs Are Willing to Risk Backing Navalny

Russia Why Russian Tech Entrepreneurs Are Willing to Risk Backing Navalny (original document) A group of Russian Internet entrepreneurs has taken the unusual and potentially risky step of speaking out publicly in support of Kremlin critic Alexei Navalny. In an open letter distributed on Aug. 7 to local media outlets, 37 leaders of Russian Web startups said they were backing Navalny’s campaign for mayor of Moscow, as a protest against corruption and other official abuses. They said they were speaking as individuals, rather than as representatives of their businesses. “The situation in Russia is deteriorating beyond reasonable limits,” Kamil Kurmakayev, a Web entrepreneur who organized the effort, tells  Bloomberg Businessweek  in an interview. He says the government’s treatment of Navalny, who is running for mayor while appealing a recent conviction on theft charges, mirrors the experience of business people who see that “in Russia, the government can do...

Cisco to lay off 4,000 employees

Cisco to lay off 4,000 employees  source: TOI NEW YORK: Cisco's earnings and revenue grew in the latest quarter as demand for its computer networking equipment increased. But CEO John Chambers called the global economy "challenging and inconsistent" and the company said it is cutting about 4,000 jobs, or about 5% of its work force. Cisco's revenue guidance  for the current quarter was weaker than Wall Street expected, and shares fell sharply in extended trading. The company's stock fell $2.51, or 9.5%, to $23.87 in extended trading after the results were released. The stock closed up 6 cents at $26.38 in the day's regular trading session. Cisco Systems  earned $2.27 billion, or 42 cents per share, in the three months that ended on July 27. That's up from $1.92 billion, or 36 cents per share, a year earlier. Adjusted earnings were 52 cents per share in the latest quarter, squeaking past Wall Street's expectations by a penny. This figure excl...

Microsoft to launch Windows 8.1 on October 18

Microsoft to launch Windows 8.1 on October 18 source: TOI SAN FRANCISCO: A tweaked version of Microsoft's Windows operating system which restores the "Start" button missed by users and updates other features will be available on October 18, the company said.  Windows 8.1  will be offered as a free download to those already using Windows 8, and comes in response to a lukewarm reception to the operating system introduced last year aimed at serving both mobile devices and PCs.  A full retail version of Windows 8.1 will also be available on the same date.  "I know a lot of folks are eager to find out when they will be able to get Windows 8.1," said a blog posting from Microsoft's Brandon LeBlanc.  LeBlanc said it would roll out worldwide starting in New Zealand just after midnight.  "Windows 8.1 brings many improvements in areas like personalization, Internet Explorer 11, search which is powered by Bing, built-in apps including a few new ones, an impro...

BSNL to set up defence telecom network by July 2015

BSNL to set up defence telecom network by July 2015 State-run telecom operator Bharat Sanchar Nigam Limited ( BSNL ) is reportedly working to set up an alternative communication network for exclusive use by the Indian defence sector. BSNL is supposed to hand over the network by July 2015. After setting up of the new network, the defence sector is likely to release the 150 MHz of spectrum in frequency range of 1700 MHz to 2000 MHz. . According to BSNL Chairman and Managing Director RK Upadhyay, the new network uses optical fibre and satellite links and is "is targeted to be completed in three years from Cabinet approval and this works out to July 2015. It's a tight schedule, but BSNL is making all efforts to meet it." BSNL is likely to begin rolling out the optical fibre cable network across 57,000 kilometres by January 2014. The telco has issued tenders for a 3,000 kilometre OFC network for the navy, which is likely to be ready by the end of next year. The ...

Optimizing land use classification using decision tree approaches

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                                Optimizing land use classification using decision tree approaches Vaibhav Walia + under guidance of DR. Sameer Saran  Indian Institute of remote sensing (NRSA), Dehradun (UA)-248 001 + Manipal institute of technology, Manipal (KA) E-mail: walia.vaibhav@yahoo.com Abstract: Supervised classification is one of the important tasks in remote sensing image interpretation, in which the image pixels are classified to various predefined land use/land cover classes based on the spectral reflectance values in different bands. In reality some classes may have very close spectral reflectance values that overlap in feature space. This produces spectral confusion among the classes and results in inaccurate classified images. To remove such spectral confusion one requires extra spectral and spatial knowledge. This report presents a decision tree classifier...

Microsoft ditching points for Xbox Live with next system update

Microsoft ditching points for Xbox Live with next system update  ( original article ) Earlier this year, Microsoft had made its intentions of  phasing out the wretched Points system  on Xbox Live rather clear, but what it didn’t outline was the timeline. Larry Hryb, Director of Programming for Xbox Live, has just announced that come the next system update, the MS Points will be eliminated. Microsoft had said earlier this year during the  announcement of the Xbox One  that the company will also be doing away with the wretched MS Points system, which had become the cause of frustration for many gamers. The issue was not just with the arbitrary conversion of real money to Points, but also when translating different currencies into Points. Since Points could only be bought in USD equivalents, international customers ended up paying more for their Points than the US counterparts due to various currency conversion factors. Microsoft plans on implementin...

The week in Tech: 5 must-know things

The week in Tech: 5 must-know things 1) Yahoo is getting a new logo — in a month Out with the old, in with the new. Yahoo is changing its logo for the first time in its 18-year history next month. A company executive told USA TODAY's Jon Swartz that Yahoo may change its typeface, its trademark color (purple) and its exclamation point in the rebranding process. But Yahoo commercials will still have the company's distinctive yodel. Yahoo will keep things interesting by unveiling a new logo every day, for 30 days, until the real logo is introduced on Sept. 4. 2) Review: Design it yourself Moto X a solid phone for consumers Last week we told you all about Motorola's new Moto X smartphone and its cool new features. But how does it stack up against its other smartphone competitors? USA TODAY's Ed Baig took the Moto X out for a test run earlier this week and gave us a first look at the pros and cons of the new phone: Good:  Driving Mode for voice-controlled...

Former Microsoft VP thought dead

Former Microsoft VP thought dead after his plane crashes into Connecticut homes Bill Henningsgaard, a former sales VP at the computing giant, is presumed dead, along with his 17-year-old son and two younger children, after his plane crashes into two homes while approaching an airport.( Read the original post here ) A former Microsoft executive, along with his 17-year-old son and two younger children, are presumed dead after the man's small plane crashed into two Connecticut homes Friday. Bill Henningsgaard, 54, held various marketing and sales positions at the computing giant -- including vice president of sales for the western United States, Australia, and New Zealand -- before leaving in the early 2000s to focus on philanthropy. He was on a trip to explore college options with his son when his plane went down while approaching Connecticut's Tweed New Haven airport. The cause of the crash has not yet been determined. An East Haven Fire Department official  told  ...

JAVA Chat App - OKok

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OKok chat OKok chat is a simple chat application developed  using java, it is meant for "one on one" chat between two people only, It uses java's " java.net " for communicating through sockets. In this post i'll be posting both the code and HOW TO'S  of running the application PART 1( The application) #Step 1: Download the application  Note :   If two people (ONE and TWO) want to chat with each other then ONE should download Server.jar and TWO should download Client.jar(or vice versa).  In short if person 1 has server.jar then person 2 should have client.jar   Also  BOTH  need to download " jarfix.exe " You can download the respective file here  1:   Server.jar  ( 7.1 KB )  2:   Client.jar  (7 KB)  3:   jarfix.exe  (63.8 KB) Things you need to know :  " IP Address " of the person having Server.jar ( click here to find your ip )   ...