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Message boards : General discussion : God, primes and the universe

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Profile Toshio Yamaguchi
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Message 67987 - Posted: 30 Jul 2013 | 23:08:30 UTC

Prime numbers are really one of THE great mysteries in my opinion. I think it's remarkable that despite having been studied for centuries (hint: Euclid's Elements, 300 BC) and them being in a sense the "atoms" of the integers (cf. Fundamental theorem of arithmetic), so many questions about prime numbers remain open. For example, as of 2013, all four of Landau's problems remain unsolved. For many specific classes of prime numbers (like Mersenne, Fermat, Wieferich or regular primes) it is still unknown whether there are infinitely many of each class. Other important unsolved problems are Andrica's conjecture or Polignac's conjecture regarding the gaps between prime numbers. And not to forget the connection between the Riemann zeta function and prime numbers (this article is also an interesting read) and the intriguing patterns the primes form. Then there is their tendency in their distribution to follow some strong rules, but at the same time to behave in a very unpredictable way (compare with Zagier's quote from 1975, see the quote below the illustration at MathWorld). As Paul Erdős said: "God may not play dice with the universe, but something strange is going on with the prime numbers."

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Message 67991 - Posted: 31 Jul 2013 | 4:50:37 UTC - in response to Message 67987.

Thank you for the post.

Message boards : General discussion : God, primes and the universe

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