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Formula for Primes, Number of Primes

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For a long time, mathematicians had been trying to see if there was a formula that could generate primes, writes Marcus du Sautoy in Music of the Primes . Euler found a curious formula that did just that. Upto a (very small) number. The formula is absurdly easy to understand: x 2 + x + 41 , for all values of x from 0 to 39 He then noticed that the formula: x 2 + x + q would spit out primes if q = 2, 3, 5, 11 and 17 when fed numbers 0 to (q – 2).   I was surprised there’s actually a formula for finding all primes. Yes, all primes. Assign any integer values to the 26 letters, a to z. Then calculate the equation below using the values you selected: If the answer is positive, then that number (the answer) is a prime. The problem with this formula, though, is that it will throw up negative results a lot of the time – those don’t count as prime numbers, obviously. But all the positive ones do. And every single prime can be found via some combo of values assigned to th...

Time is Money

William Poundstone started off his book Fortune’s Formula in the age before live transmission of sports and before long distance phone calls. That meant there was a few minutes delay between the time a race at the racetrack got over and the times the bookies got to know the outcome. In theory, says Poundstone: “A customer who learned the winner before the bookmakers did could place bets on a horse that had already won.” Of course, it worked the other way too: a bookmaker who knew the result before others would be quite happy to accept bets on a horse that he knew had lost! A man named John Payne spotted this opportunity and started a wire service to speed up the communication of race results to anyone who’d pay for it: “Payne stationed an employee at the local racetrack. The instant a horse crossed the finish line, the employee used a hand mirror to flash the winner, in code, to another employee in a nearby tall building. This employee telegraphed the results.” In the pres...

Do Formulas Apply Outside of Physics?

Thanks to the ongoing recession, it’s easy to find people today who say that formulas (and the associated maths) don’t work in finance. I don’t know if that’s becoming the widespread belief in finance today, but if it is, it would make it hard for the quants (the guys who apply the maths to finance and come up with the formulas) to find jobs. Then again, the same feeling persisted more than a decade back when a huge hedge fund, LTCM, failed and threatened to take down the system with it. Even back then, there was a comment in the book, When Genius Failed , by a guy who thought that quants picked a physics formula to “jam into finance”! Another quote which I liked questioned the accuracy of formulas in a very funny way: this one by Max Bublitz, a former investment banker: “You take Monica Lewinsky, who walks into Clinton’s office with a pizza. You have no idea where that’s going to go. Yet if you apply math to it, you come up with a thirty-eight percent chance she’s going to go down ...