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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 4 Jan 2018
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    2⁷⁷²³²⁹¹⁷-1 is the largest known prime number and was discovered on Jan 3, 2018. It's substantially easier to find primes of the form 2ᵖ-1, also called Mersenne Primes. Here's why: http://fermatslibrary.com/s/a-really-trivial-proof-of-the-lucas-lehmer-test#email-newsletter …pic.twitter.com/8Dl6Zm1xtS

    5:55 AM - 4 Jan 2018
    • 2,040 Retweets
    • 4,025 Likes
    • Yue Ying Yin lmustafa Musician_Logos HeroinHerbert Micki & Charles Oleg Pankratov frozflame maki JP
    30 replies 2,040 retweets 4,025 likes
      1. New conversation
      2. Glyn!‏ @glyndekari 4 Jan 2018
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        it has no practical use we just like finding new primes

        1 reply 0 retweets 15 likes
      3. ven‏ @vengarioth 4 Jan 2018
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        Replying to @glyndekari @fermatslibrary

        modern cryptography is entirely built on factorization of large prime numbers. also algorithms for procedural generation used in games often use irrational numbers or large primes as a source of randomness

        1 reply 3 retweets 47 likes
      4. 4 more replies
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      2. DℝOℕ∈‏ @d_r_o_n_e 4 Jan 2018
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        Replying to @fermatslibrary

        If anyone wonders how many digits are there: 1 + floor(77232917·lg2) = 23249425 digits

        1 reply 2 retweets 19 likes
      3. Truls Henriksson‏ @thekebabrulle 4 Jan 2018
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        Replying to @d_r_o_n_e @fermatslibrary

        Is that formula exact?

        1 reply 0 retweets 0 likes
      4. 2 more replies
      1. Mattia Pezzali‏ @leshpretoria 4 Jan 2018
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        Replying to @fermatslibrary @jamesgrime

        How is it possible that such big numbers can't be divided?

        2 replies 0 retweets 3 likes
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      1. Michiel  ☁️‏ @Michielstock 11 Jan 2018
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        Replying to @fermatslibrary

        I read in @JSEllenberg's book that many properties of prime number make sense if you just think of them as randomly distributed. Intuitively it feels right that 2^{p-1} has a high 'chance' of being prime.

        0 replies 1 retweet 1 like
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      1. New conversation
      2. Pablo Miguez‏ @pablomiguezdm 4 Jan 2018
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        Replying to @fermatslibrary

        how many digits does it have?

        1 reply 0 retweets 0 likes
      3. Phil Marsden‏ @phil_marsden 4 Jan 2018
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        Replying to @pablomiguezdm @fermatslibrary

        Roughtly 2.3 million I reckon.

        1 reply 0 retweets 1 like
      4. End of conversation
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      2. Brian La Roux‏ @BrianLaRoux 3 Mar 2018
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        Replying to @josefbetancourt @fermatslibrary

        You probably wouldn't want to use Mersenne primes to make a public/private key for the RSA algorithm, simply because they're easily guessed. But if a publicly-known large prime needed to be chosen for an algorithm, a Mersenne could be useful.

        0 replies 0 retweets 0 likes
      3. End of conversation

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