# 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.

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

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

2. ### noneGuest

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

3. ### XPDGuest

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

Heh I second that

XPD, Jul 24, 2007
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
5. ### XPDGuest

<> 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
6. ### JerryGuest

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

Jerry, Jul 25, 2007
7. ### Don HillsGuest

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

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!"

Don Hills, Jul 25, 2007
8. ### Yeah RightGuest

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

Dons' different, he adds a bit of variety to our groups.

Yeah Right, Jul 26, 2007