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    Sexy Prime

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    Jesus Zelaya Contreras
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    Sexy Prime

    Uploaded by

    Jesus Zelaya Contreras
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    Paper about the interesting number called sexy prime

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    Paper about the interesting number called sexy prime

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    144 views3 pages

    Sexy Prime

    Uploaded by

    Jesus Zelaya Contreras
    Paper about the interesting number called sexy prime

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 3

    Sexy prime

    In mathematics, sexy primes are prime numbers that differ from each other by six. For example, the numbers 5 and 11 are both sexy
    primes, because 11 minus 5 is 6. If p + 2 or p + 4 (where p is the lower prime) is also prime, then the sexy prime is part of a prime
    triplet.

    The term "sexy prime" is a pun stemming from theLatin word for six: sex.

    Contents
    n# notation
    Types of groupings
    Sexy prime pairs
    Sexy prime triplets
    Sexy prime quadruplets
    Sexy prime quintuplets
    See also
    References
    External links

    n# notation
    As used in this article,n# stands for the product 2 · 3 · 5 · 7 · … of all the primes ≤n.

    Types of groupings

    Sexy prime pairs


    The sexy primes (sequences A023201 and A046117 in OEIS) below 500 are:

    (5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59),
    (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137),
    (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233),
    (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317),
    (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449),
    (457,463), (461,467).

    As of May 2009 the largest known sexy prime was found by KenDavis and has 11,593 digits. The primes are (p, p+6) for

    p = (117924851 × 587502 × 9001# × (587502 × 9001# + 1) + 210) × (587502 × 9001# −


    1)/35 + 5.[1]

    9001# = 2×3×5×...×9001 is aprimorial, i.e., the product of primes ≤ 9001.

    Sexy prime triplets


    Sexy primes can be extended to larger constellations. Triplets of primes (p, p + 6, p + 12) such that p + 18 is composite are called
    sexy prime triplets. Those below 1000 are ( A046118, A046119, A046120):

    (5,11,17), (7,13,19), (17,23,29), (31,37,43), (47,53,59), (67,73,79), (97,103,109),


    (101,107,113), (151,157,163), (167,173,179), (227,233,239), (257,263,269), (271,277,283),
    (347,353,359), (367,373,379), (557,563,569), (587,593,599), (607,613,619), (647,653,659),
    (727,733,739), (941,947,953), (971,977,983).

    As of 2013 the largest known sexy prime triplet, found by Ken Davis had 5132 digits:

    p = (84055657369 · 205881 · 4001# · (205881 · 4001# + 1) + 210) · (205881 · 4001# - 1) / 35


    + 1.[2]

    Sexy prime quadruplets


    Sexy prime quadruplets (p, p + 6, p + 12, p + 18) can only begin with primes ending in a 1 in their decimal representation (except for
    the quadruplet with p = 5). The sexy prime quadruplets below 1000 are ( A023271, A046122, A046123, A046124):

    (5,11,17,23), (11,17,23,29), (41,47,53,59), (61,67,73,79), (251,257,263,269),


    (601,607,613,619), (641,647,653,659).

    In November 2005 the largest known sexy primequadruplet, found by Jens Kruse Andersen had 1002 digits:

    p = 411784973 · 2347# + 3301.[3]

    In September 2010 Ken Davis announced a 1004-digit quadruplet withp = 23333 + 1582534968299.[4]

    Sexy prime quintuplets


    In an arithmetic progression of five terms with common difference 6, one of the terms must be divisible by 5, because 5 and 6 are
    relatively prime. Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence of sexy primes is possible.

    See also
    Cousin prime (two primes that differ by 4)
    Prime k-tuple
    Twin prime (two primes that differ by 2)

    References
    1. Ken Davis, "11,593 digit sexy prime pair"(http://tech.groups.yahoo.com/group/primenumbers/message/20207)
    .
    Retrieved 2009-05-06.
    2. Jens K. Andersen, "The largest known CPAP-3" (https://web.archive.org/web/20130502162216/http://users.cybercity
    .
    dk/~dsl522332/math/cpap.htm#k3). Retrieved 2014-06-13.
    3. Jens K. Andersen, "Gigantic sexy and cousin primes"(https://groups.yahoo.com/group/primeform/message/6637)
    .
    Retrieved 2009-01-27.
    4. Ken Davis, "1004 sexy prime quadruplet"(http://tech.groups.yahoo.com/group/primenumbers/message/21783)
    .
    Retrieved 2010-09-02.

    Weisstein, Eric W. "Sexy Primes". MathWorld. Retrieved on 2007-02-28 (requires compositep+18 in a sexy prime
    triplet, but no other similar restrictions)

    External links
    Grime, James. "Sexy Primes (and the only sexy prime quintuplet)"
    . Numberphile. Brady Haran.

    Retrieved from "https://en.wikipedia.org/w/index.php?title=Sexy_prime&oldid=865866559


    "

    This page was last edited on 26 October 2018, at 18:01(UTC).

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