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New world record prime number discovered

The GIMPS Project has announced the discovery of the largest known prime number to date, the Mersenne prime 257885161-1. At 17,425,170 digits, it is more than four million digits longer than the previous record, set in 2008. The news coverage of this discovery was decent considering the subject matter, with the occasional facepalm-inducing moment, such as NBC News declaring it the largest prime number. I think an old mathematician named Euclid might have something to say about that if he were still around. One of the more notable aspects of this story was how quickly the primality of this number... Continue reading

Posted Feb 5, 2013 at Superconductor

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The safest prime

The 79911-digit number 183027 x 2265441 - 1 is the world's "safest" prime, and has just passed the two-year anniversary of its discovery. Recall that a safe prime is an odd prime p where (p-1)/2 is also prime. What's so special about safe primes? When working in the multiplicative group mod p, it is easy to find a generator g that generates all of the values in the group. Some cryptographic protocols such as SRP depend on this property to prevent an attacker from distinguishing between values that could be generated by g and those that could not. If p... Continue reading

Posted Mar 22, 2012 at Superconductor

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