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Keyword: primes

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  • Mathematicians Discover Prime Conspiracy

    03/14/2016 5:28:27 PM PDT · by MtnClimber · 58 replies
    Quanta Magazine ^ | 13 Mar, 2016 | Erica Klarreich
    A previously unnoticed property of prime numbers seems to violate a longstanding assumption about how they behave. o mathematicians have uncovered a simple, previously unnoticed property of prime numbers — those numbers that are divisible only by 1 and themselves. Prime numbers, it seems, have decided preferences about the final digits of the primes that immediately follow them. Among the first billion prime numbers, for instance, a prime ending in 9 is almost 65 percent more likely to be followed by a prime ending in 1 than another prime ending in 9. In a paper posted online today, Kannan Soundararajan...
  • Prime Diffie-Hellman Weakness May Be Key to Breaking Crypto

    10/18/2015 12:19:56 PM PDT · by Mycroft Holmes · 20 replies
    ThreadPost ^ | October 16, 2015 | Michael Mimoso
    The great mystery since the NSA and other intelligence agencies’ cyber-spying capabilities became watercooler fodder has not been the why of their actions, but the how? For example, how are they breaking crypto to decode secure Internet communication? A team of cryptographers and computer scientists from a handful of academic powerhouses is pretty confident they have the answer after having pieced together a number of clues from the Snowden documents that have been published so far, and giving the math around the Diffie-Hellman protocol a hard look. The answer is an implementation weakness in Diffie-Hellman key exchanges, specifically in the...
  • RSA-640 Factored

    11/09/2005 4:44:53 AM PST · by zeugma · 19 replies · 788+ views
    MathWorld News ^ | November 8, 2005 | Eric W. Weisstein
    RSA-640 Factored By Eric W. Weisstein November 8, 2005--A team at the German Federal Agency for Information Technology Security (BSI) recently announced the factorization of the 193-digit number 310 7418240490 0437213507 5003588856 7930037346 0228427275 4572016194 8823206440 5180815045 5634682967 1723286782 4379162728 3803341547 1073108501 9195485290 0733772482 2783525742 3864540146 9173660247 7652346609 known as RSA-640. The team responsible for this factorization is the same one that previously factored the 174-digit number known as RSA-576 (MathWorld headline news, December 5, 2003) and the 200-digit number known as RSA-200 (MathWorld headline news, May 10, 2005). RSA numbers are composite numbers having exactly two prime factors (i.e.,...