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New Largest Prime

posted by janrinok on Wednesday October 23 2024, @09:32PM   Printer-friendly
from the 2-3-5-7-11-13-17-19-23-29-... dept.

looorg writes:

https://www.mersenne.org/primes/?press=M136279841

The Great Internet Mersenne Prime Search (GIMPS) has discovered the largest known prime number, 2136,279,841-1, having 41,024,320 decimal digits. Luke Durant, from San Jose, California, found the prime on October 12th.

The new prime number, also known as M136279841, is calculated by multiplying together 136,279,841 twos, and then subtracting 1. It is over 16 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 52nd known Mersenne prime ever discovered, each increasingly more difficult to find. Mersenne primes were named for the French monk Marin Mersenne, who studied these numbers more than 350 years ago. GIMPS, founded in 1996, has discovered the last 18 Mersenne primes. Volunteers download a free program to search for these primes, with a $3000 award offered to anyone lucky enough to find a new prime. Prof. Chris Caldwell founded an authoritative web site on the largest known primes which is now maintained by volunteers, and has an excellent history of Mersenne primes.

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  • (Score: 3, Insightful) by pTamok on Thursday October 24 2024, @07:41AM (1 child)

    by pTamok (3042) on Thursday October 24 2024, @07:41AM (#1378434)

    It allows you to determine another perfect number.

    https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Barrus_and_Clark)/01%3A_Chapters/1.16%3A_Perfect_Numbers_and_Mersenne_Primes [libretexts.org]

    There is also a proposed 'post-Quantum' cryptosystem based upon the use of Mersenne primes: Mersenne-756839 (PDF) [nist.gov]

    It has already been 'successfully' attacked. Exploiting Decryption Failures in Mersenne Number Cryptosystems [kuleuven.be], success being defined as:

    Our attack is able to extract a good estimate of the secrets using 212 decryption failures, corresponding to 274 failing ciphertexts in the original scheme.
    Subsequently the exact secrets can be extracted in O(246) quantum computational steps.

    But the thing to remember is that attacks tend to get better over time.

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  • (Score: 2) by DannyB on Thursday October 24 2024, @07:47PM

    by DannyB (5839) Subscriber Badge on Thursday October 24 2024, @07:47PM (#1378530) Journal

    It allows you to determine another perfect number.

    There are perfect numbers. But there are no perfect prime ministers.

    A perfect prime minister would be one whose length of tenure was equal to the sum of its proper divisors. But since the minister is prime it doesn't have any proper divisors other than one. Thus there are no perfect prime ministers.

    --
    If we sing a slaying song tonight, what tools will be used for the slaying?