At Play With J

The Google Test Eugene McDonnell

Eemcd@aol.com

{first 10-digit prime found in consecutive digits of e}.com

Google apparently trusted that some among those passing the poster would understand it, and of these some might be intrigued enough by it to see if they could find that prime, and perhaps some of them might use it to go to the resulting web address. Those who did go the whole route would then find themselves with this message:

Congratulations. You have made it to level 2. Go to www.linux.org and enter Bobsyouruncle as the login and the answer to this equation as the password. F(1)= 7182818284 F(2)= 8182845094 F(3)= 8747135266 F(4)= 7427466391 F(5)=__________

Congratulations. Nice work. Well done. Mazel tov. You've made it to Google Labs and we are glad you are here. One thing we learned while building Google is that it's easier to find what you're looking for if it comes looking for you. What we're looking for are the best engineers in the world. And here you are. As you can imagine, we get many, many resumes every day, so we developed this little process to increase the signal to noise ratio. We apologize for taking so much of your time just to ask you to consider working with us. We hope you'll feel it was worthwhile when you look at some of the interesting projects we're developing right now. You'll find links to more information about our efforts below, but before you get immersed in machine learning and genetic algorithms, please send your resume to us at problem-solver@google.com. We're tackling a lot of engineering challenges that may not actually be solvable. If they are, they'll change a lot of things. If they're not, well, it will be fun to try anyway. We could use your big, magnificent brain to help us find out.

You now have all you need to know to dazzle Google with your magnificent brain. I haven't spoiled it for you, so you can legitimately do it on your own. I will, however, give you a similar puzzle, in two parts, and will solve it for you. It uses the digits of pi.

Problem 1: Finding 10-digit primes

The first problem is to find among the digits of pi a ten-digit sequence that, when evaluated in base ten, is a prime number, and is the eighth such. Your first problem, then, is to obtain the first few hundred or so digits of pi. We're in luck! The great Indian mathematician Ramanujan used the theory of complex multiplication of elliptic curves to give a number of beautiful formulas for pi's digits, and a variation of this technique was discovered by the ingenious Chudnovsky brothers, from New York City by way of Kiev. A J function for their method is: