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New Mersenne Prime Discovered, Largest Known Prime Number: 2^74,207,281 - 1 (mersenne.org)

Posted by Soulskill on from the that's-my-phone-number dept.

Dave Knott writes: The Great Internet Mersenne Prime Search (GIMPS) has discovered a new largest known prime number, 2^74,207,281-1, having 22,338,618 digits. The same GIMPS software recently uncovered a flaw in Intel's latest Skylake CPUs, and its global network of CPUs peaking at 450 trillion calculations per second remains the longest continuously-running "grassroots supercomputing" project in Internet history. The prime is almost 5 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 49th known Mersenne prime ever discovered, each increasingly difficult to find.

11 of 132 comments (clear)

  1. Mental note by aaarrrgggh · · Score: 4, Funny

    Thanks, now I need to change private key.

  2. Re:PrimeCoins by suso · · Score: 4, Insightful

    There is a US$3000 award for the finder.

    And a $3000 power bill for those who don't find it.

  3. Re:"each increasingly difficult to find." by Pseudonym · · Score: 4, Informative

    Here you go: S. Wagstaff, "Divisors of Mersenne numbers," Math. Comp., 40:161 (January 1983) 385--397. MR 84j:10052

    It's true that we don't know for sure, but it's not true that we have no fucking idea.

    --
    sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
  4. Re:PrimeCoins by Livius · · Score: 5, Funny

    Obviously prime posts start with the second one.

  5. Re:PrimeCoins by DesertNomad · · Score: 4, Informative

    this is likely true as the number 1 is not a prime number. https://primes.utm.edu/notes/f...

  6. Re:Rare Primes? by Anonymous Coward · · Score: 5, Informative

    It's not so much that Mersenne numbers are much more likely to be prime than other odd numbers of their size. It's that there is a special-purpose primality test just for Mersenne numbers that is tons more efficient than verifying other primes of similar size.

  7. It's small. by Kwyj1b0 · · Score: 5, Funny

    It's still smaller than the box Amazon Prime uses to send me a toothpick.

  8. 22,338,618 digits by mejustme · · Score: 5, Interesting

    How "big" is 22,338,618 digits? Text file containing the prime is 22.8 MiB in size. http://www.mersenne.org/primes...

    1. Re:22,338,618 digits by craigm4980 · · Score: 4, Insightful

      The number is 2^74,207,281-1, thus its exactly 74,207,280 bits long and all those bits are 1. That's 9,275,910 bytes, or roughly 9MiB. When talking about mersenne primes on a tech site, using base 10 versions encoded as ascii (or utf-8, its the same for that subset) seems like an odd measure of size.

  9. Re:Rare Primes? by Anonymous Coward · · Score: 4, Insightful

    Uninteresting fact.

    If 2^n-1 is represented in binary then n will be the number of set bits.
    That means that if n can be divided by m then 2^n-1 can be divided by 2^m-1. (For example 2^15-1 = 32767 and can be divided by 2^3-1 and 2^5-1.)
    From the headline we can tell that 74,207,281 is a prime, otherwise 2^74,207,281-1 wouldn't be a prime.

  10. Re:"each increasingly difficult to find." by Petronius+Arbiter · · Score: 4, Informative

    Math is also fascinating because of how it can often work around impossibility proofs.

    E.g., what class of polynomials is solvable depends on what elementary functions are allowed. With Jacobi theta functions, you can exactly solve quintics.

    http://mathoverflow.net/questi...

    For another example, with cosine and acos, you can exactly solve cubic polynomials, w/o using cube roots. Better, if the solutions are real, then the solution does not require imaginary numbers, unlike if you solve with cube roots.