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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

927.0. "Are my numbers prime ? Help me..." by FNYADG::HUDELOT () Thu Sep 08 1988 09:58

	I have to find very large prime numbers. I heard from the JACOBI
algorithm that checks if an integer is prime, but I can't find it. Is
there another algorithm that makes the same?

        Any information or any algorithm would be welcome. Please mail me
on FNYADG::HUDELOT or send a Note.

        Thanks,

               Patrick (I'm NOT a mathematician...)
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927.1A good recent referenceCTCADM::ROTHIf you plant ice you'll harvest windThu Sep 08 1988 16:337
    There's a recent book by Hans Riesel, published by Birkhauser
    on prime numbers and computer algorithms for them.  It will probably
    supply you with all the information you need - he gives PASCAL programs as
    well a simple theory for factorization algorithms and tests for
    primality.

    - Jim
927.2CLT::GILBERTmultiple inheritence happensFri Sep 09 1988 10:101
    See note 2.8.  BTW, does anybody have a more recent list?
927.3list from AMSCTCADM::ROTHIf you plant ice you'll harvest windFri Sep 09 1988 11:0911
�   See note 2.8.  BTW, does anybody have a more recent list?

    The most recent list I know of (in published form) is available from
    the AMS - it appeared in the past year or so.  Though I don't have the
    exact publication title, I can look it up.  It would be mentioned in
    the Notices of the AMS most likely.

    This list contains not only Mersenne primes, but many others with
    interesting structure.

    - Jim
927.442735042735042735042735042735043 big enough?POOL::HALLYBThe smart money was on GoliathMon Sep 12 1988 17:218
    I believe the JACOBI reference is in the _Scientific American_ issue
    that described the RSA one-way encryption algorithm.  Does anybody
    remember which issue?
    
    Re: .0 -- just how big are these numbers?  10 digits? 40 digits? 100? 400?
    And how many do you need?

      John
927.542735032735042735042735042735043 not big enough...FNYADG::HUDELOTTue Sep 13 1988 04:2118
    Re: .4 -- You're right, I need these prime number for an RSA
    implementation. I think I will use 240 binary digits= 73 decimal
    digits (or I think so).
    
    Re: .2 and .3 -- I want to check if *very large* number so I need
    algorithms, I can't do comparisons nor use Euler_Fermat in this
    case. (see .0).
    
    I wrote note 243 in security_information conference (HUMAN_SECURITY).
    You will see there in what my job consist in, who I am ... and why
    my english is so bad.
    
    Anyway, thank you for your interest in this note. I don't have the
    _Scientific American_ issue and I would like to find this algorithm.
    I have a version that gave me very bad results (2 per cent of error
    checking!!) so I guess that my implementation does not be very good.
    
    Thank you again, Patrick.