veRified: Interesting FACTORISE program, by trial division. + Fermat s method.Casio fx-82 MS schools

Discussion in 'NZ Computing' started by don.lotto@paradise.net.nz, Jul 24, 2007.

  1. Guest

    On Jul 17, 4:09 pm, wrote:

    FERMATS factorise method a^2-N=b^2, hand calc fx-82
    MS. Casio

    not. bcc; tom nzmm nzm andr sto, riscos- dnghm,

    one key press per trial.
    has anyone seen this method before.?

    ....
    Adept FACTORISE program by Trial Division.
    Not stored program but MultiStep, Casio Fx-82 MS,
    schools sci-calc.

    By Donald S. McDonald.
    23-7-2007, Wellington, New Zealand.


    Calculate number.. # SHIFT STORE A
    While even / 2 SHIFT STORE A
    write factor, cofactor
    = = ... until odd or
    ( unity ... end power 2^n.)

    ALPHA A / ( ALPHA A / ANS +2 divide by odd integers
    = = ... iterate watching, 1 keypress per trial

    Until Decimal part = 0 or ANS ~ sqrt A = v A
    Write this cofactor

    ALPHA A / ANS SHIFT STORE B write factor
    ALPHA A / ALPHA B SHIFT STORE A write cofactor,
    prog will attempt to further reduce A.
    While Decimal part = 0
    = ... until too far Decimal part # 0
    repeat factor? Write fact, cofactor.

    * ALPHA B SHIFT STORE A too far,
    not repeat factor-strike out.
    Write estimate v A, 2 significant figures.

    / ALPHA B =

    ALPHA A / ( ALPHA A / ANS +2 divide by odd
    integers, iterate watching, etc.
    As above.

    Until decrement quotient between steps < 2.

    RCL A is greatest odd prime factor.
    RCL B is 2nd greatest odd prime factor.

    Examples 381 9603 *4
    385 9603 *16
    387 9603 *64.

    This test for repeated factor is very fiddly tricky.
    e.g SHIFT STORE , e.g. alpha A, B.

    If trial division (prog Adept) is slow to yield any
    small factors,..Then Fermat's method may split into
    larger relatively close (odd) factors..

    Either method can ultimately prove primality but is
    very inefficient.
    Fermat's little theorem is a useful step to proving an
    integer composite, i.e. NOT PRIME.

    FERMAT's factorise method.
    Initial steps same as Adept.

    Calculate number.. # SHIFT STORE A
    While even / 2 SHIFT STORE A
    write factor, cofactor
    = = ... until odd or
    ( unity ... end power 2^n.)

    Sqrt A =
    V ( ceil^2 - alpha A SHIFT STORE Y
    If Decimal part = 0, squarest factor or perfect
    square; skip to until below.

    V ( ( v ( ANS^2 + alpha A ) +1 ) ^2 - alpha A
    SHIFT STORE Y

    = .... Iterate watching
    Until Decimal part = 0

    V (ANS^2 + alpha A ) - ANS SHIFT STORE C
    Write this factor, (X - Y).

    Alpha A / ANS SHIFT STORE A
    Write, this is cofactor, (X+Y).

    Factors are not necessarily prime-can be tested
    further,... As from top of FERMATs page.

    ( e.g. RCL C SHIFT STORE A )
    Same example/s, as above.

    Important. Iterative step is one keypress per trial.

    ...........

    enter number etc.
    take out factors 2. .. 4, 8... reduce to odd.

    SHIFT STORE A
    sqrt alpha A =

    v(ceil ^2 - alpha A) =

    v (( v (ANS^2 + alpha A) +1 )^2 - alpha A

    = = = = .............. iterate looking.
    until decimal part = zero.

    hence..
    A = X^2 - Y^2 = (X-Y)(X+Y).
    factors.
    ...................

    don.mcdonald.


    Interesting FACTORISE program, by trial division.
    Casio fx-82 MS schools sci-calc.

    Calculate number #
    SHIFT STORE A
    Alpha A / ( alpha A / ANS +2
    = = = ...........
    iterate watching..
    Until decimal part = 0
    THEN alpha A / ANS =


    Continue above from
    SHIFT STORE A, etc.
    .............


    Don.mcdonald nz 14/7/07.
    often works with 7-digit phone numbers.
    mcd page 320.

    st cuth 389-9603 prime, mcc.. 526-9603 prime ??
    sincerely, Thank you,

    Don S. McDonald ... view my profile/ + more
    articles. [click]
     
    , Jul 24, 2007
    #1
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  2. none Guest

    Re: veRified: Interesting FACTORISE program, by trial division. +Fermat s method.Casio fx-82 MS schools sci-calc.

    wrote:
    "Verified Interesting" ?

    /me doubts that somehow
     
    none, Jul 24, 2007
    #2
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  3. XPD Guest

    "none" <> wrote in message
    news:46a664c3$...
    > wrote:
    > "Verified Interesting" ?
    >
    > /me doubts that somehow


    Heh I second that :)
     
    XPD, Jul 24, 2007
    #3
  4. Guest

    On Jul 24, 3:48 pm, wrote:
    > On Jul 17, 4:09 pm, wrote:
    >
    > FERMATS factorise method a^2-N=b^2, hand calc fx-82
    > MS. Casio


    > don.mcdonald.


    > Don.mcdonald nz 14/7/07.
    > often works with 7-digit phone numbers.


    381 9603 =3*31*67*613
    n+119^2 = 1958^2.

    385 9603 = 11*19*59*313

    387 9603 = 3^3*7*13*1579.
    Q E D.
    > mcd page 320.
    >
    > st cuth 389-9603 prime, mcc.. 526-9603 prime ??
    > sincerely, Thank you,
    >
    > Don S. McDonald ... view my profile/ + more
    > articles. 2400.. [click]
     
    , Jul 25, 2007
    #4
  5. XPD Guest

    <> wrote in message
    news:...
    > On Jul 24, 3:48 pm, wrote:
    >> On Jul 17, 4:09 pm, wrote:
    >>
    >> FERMATS factorise method a^2-N=b^2, hand calc fx-82
    >> MS. Casio

    >



    Hi Don,

    As much as this info is probably invaluable to you and others who love calcs
    etc, noone in nz.comp really seems to care/take notice except to ridicule
    you.
    So one of two things could be good here..... 1) Stop cross posting to
    nz.comp or 2) If youre going to post, then at least explain what the hell
    it all means to those of use who have no idea and maybe we might take some
    interest.

    Thanks :)

    PS: Im not being the "net police", just putting forward my view/opinion
    which you may or may not give a hoot about :) Your choice.
     
    XPD, Jul 25, 2007
    #5
  6. Jerry Guest

    Re: veRified: Interesting FACTORISE program, by trial division. +Fermat s method.Casio fx-82 MS schools sci-calc.

    XPD wrote:
    > <> wrote in message
    > news:...
    >> On Jul 24, 3:48 pm, wrote:
    >>> On Jul 17, 4:09 pm, wrote:
    >>>
    >>> FERMATS factorise method a^2-N=b^2, hand calc fx-82
    >>> MS. Casio

    >
    >
    > Hi Don,
    >
    > As much as this info is probably invaluable to you and others who love calcs
    > etc, noone in nz.comp really seems to care/take notice except to ridicule
    > you.
    > So one of two things could be good here..... 1) Stop cross posting to
    > nz.comp or 2) If youre going to post, then at least explain what the hell
    > it all means to those of use who have no idea and maybe we might take some
    > interest.
    >
    > Thanks :)
    >
    > PS: Im not being the "net police", just putting forward my view/opinion
    > which you may or may not give a hoot about :) Your choice.
    >


    Don's posts are OK, no one seems to mind. Some might think that there
    are some people a lot more annoying than Don :p
     
    Jerry, Jul 25, 2007
    #6
  7. Don Hills Guest

    Re: veRified: Interesting FACTORISE program, by trial division. +

    In article <46a715f8$>,
    Jerry <> wrote:
    >
    >Don's posts are OK, no one seems to mind. Some might think that there
    >are some people a lot more annoying than Don :p


    His post a while back about Iridium flares was useful to me, I took the kids
    outside the next night and we saw one.

    --
    Don Hills (dmhills at attglobaldotnet) Wellington, New Zealand
    "New interface closely resembles Presentation Manager,
    preparing you for the wonders of OS/2!"
    -- Advertisement on the box for Microsoft Windows 2.11 for 286
     
    Don Hills, Jul 25, 2007
    #7
  8. Yeah Right Guest

    On , , Wed, 25 Jul 2007 21:21:10 +1200, Re: veRified: Interesting
    FACTORISE program, by trial division. + Fermat s method.Casio
    fx-82 MS schools sci-calc., Jerry <>
    wrote:

    >XPD wrote:
    >> <> wrote in message
    >> news:...
    >>> On Jul 24, 3:48 pm, wrote:
    >>>> On Jul 17, 4:09 pm, wrote:
    >>>>
    >>>> FERMATS factorise method a^2-N=b^2, hand calc fx-82
    >>>> MS. Casio

    >>
    >>
    >> Hi Don,
    >>
    >> As much as this info is probably invaluable to you and others who love calcs
    >> etc, noone in nz.comp really seems to care/take notice except to ridicule
    >> you.
    >> So one of two things could be good here..... 1) Stop cross posting to
    >> nz.comp or 2) If youre going to post, then at least explain what the hell
    >> it all means to those of use who have no idea and maybe we might take some
    >> interest.
    >>
    >> Thanks :)
    >>
    >> PS: Im not being the "net police", just putting forward my view/opinion
    >> which you may or may not give a hoot about :) Your choice.
    >>

    >
    >Don's posts are OK, no one seems to mind. Some might think that there
    >are some people a lot more annoying than Don :p


    Dons' different, he adds a bit of variety to our groups.
     
    Yeah Right, Jul 26, 2007
    #8
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