By Daisuke Wakabayashi 

The rivalry between Apple Inc. and Google Inc. to dominate the smartphone business is fueling the technology industry's newest talent search: software prodigies as young as 13 who are creating apps for their mobile devices.

Grant Goodman sensed an opportunity when Apple removed the preloaded YouTube app from its iPhones last year. He quickly built an advertising-free app called Prodigus to play online videos "fast with no compromises."

Prodigus, Grant explains, was his second iPhone app. He recently built a third, a game called "iTap That," and incorporated a company, Macster Software Inc. to manage the business. Next week, the 14-year-old will take a break from his business to start high school in Glen Head, N.Y.

"If you start young, you will have an advantage over people who start in their 20s," he said. "Your brain has more plasticity when you're younger."

Grant is among a generation of teenage developers seizing opportunities afforded by the spread of smartphones and the ready market for their work through the app stores. Overall, Google has paid developers more than $5 billion over the last year, and Apple paid about $10 billion over the same period--and $20 billion since it opened its app store in 2008.

Software wunderkinds are being courted by Apple and Google to write for their mobile-operating systems. Apple in 2012 lowered the minimum age to attend its developer conference to 13, from 18, and made the younger teens eligible for scholarships that waive the $1,600 registration fee. Minors claimed roughly half of the 200 scholarships at this year's conference, where Apple introduced a new programming language, Swift, that streamlines the app-making process.

Google started its own youth program at its Google I/O developer conference in June. It hosted 200 children between the ages of 11 and 15 for a half-day, introducing them to some basic tools used by its developers.

Grant, an Apple scholarship winner, has created an app for Google Glass that displays remaining battery power of the Web-connected eyewear. But he said he prefers making apps for Apple's iOS devices because he is "obsessed" with the iPhone maker and its emphasis on simplicity.

Mother Becky Goodman says paying for summer camps for programming and computer equipment is a financial sacrifice, but worth it to see Grant happy and fulfilled. "We're not emotionally invested in him being the next Mark Zuckerberg," she said. "We just want him to be happy."

Nick D'Aloisio is a hero to many of whiz kids. Now 18, Mr. D'Aloisio last year sold his news-summarizing app Summly to Yahoo Inc. for $30 million. At Apple's June conference, Mr. D'Aloisio won a design award for a different news-reading app he developed at Yahoo.

"I hope that's me one day," said 16-year-old Douglas Bumby, as he watched Mr. D'Aloisio accept the award. Douglas drove 14 hours from Langley, B.C., with his grandparents to attend the conference in San Francisco. He spent more than 70 hours honing the app about himself that was part of the scholarship application, adding features such as a counter that tracked his age to the second.

Douglas's first app--Just Go!, a stopwatch for runners--became available in the App Store during the conference. The app is listed under his grandfather's name because he is only 16.

Developers younger than 18 years old can't publish apps in Apple's App Store, so many children register using a parent or guardians name. Google has no age restrictions for its Google Play store, but a developer needs to register an account with a credit card--something that many children don't have.

Douglas said he is sometimes mocked at school as a nerd, but enjoyed being around tech-savvy teens at the conference. He also found a business partner in 17-year-old Jason Pan from Australia.

The pair quickly formed a company, Apollo Research, and set to work on a collaboration app they're calling Slate. But Douglas said it is still difficult for young developers to get taken seriously by investors or customers. "I kind of wish I was older," he mused.

Twenty-one-year-old Sarah Rust stood out among Apple's mostly male student developers. Unlike her peers who are weighing whether to skip college, the University of North Carolina student and Apple scholarship winner is in no rush to start her career and is considering pursuing a master's degree in computer science. But she's been impressed by her peers' drive.

"They are incredibly smart, probably smarter than most adults," she said. "Age isn't a requirement to do well."

Ahmed Fathi, 15, said he taught himself how to create iPhone apps in Egypt. "Even my computer teacher has no idea what programmers do," he said. "My friends think I'm crazy. They often ask 'what the hell are you doing?' "

Ahmed said he became interested in programming after an uncle taught him how to create websites two years ago. He learned how to build mobile apps by watching YouTube videos and combing Stack Overflow, a question-and-answer site for programmers. This month, he published Tweader, an app that reads Tweets aloud for drivers or bikers, in the App Store.

Attending the conference was eye opening. He spent time touring San Francisco, Apple's campus and Stanford University. He also participated in local "hackathons"--intense collaboration sessions to create new software.

"People here care about technology," Ahmed said.

Write to Daisuke Wakabayashi at Daisuke.Wakabayashi@wsj.com

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