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Old 2021-09-23, 10:34   #12
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

32×131 Posts
Smile more calculations

Hi again all,

I have probably done over 50 quick calculations for factordb.com. In My Humble Opinion, this is a useful database. Now we know that a C74 is a P22 times a P24 times a P29. Specifically,

(2123766^17-1)/4830869344730522132314982799853985 <74> =
3995338558734555154151<22> · 483489332374281832645177<24> · 38980509326442350080033766609<29>

this calculation took 135 seconds on my Intel i7, 2.93 GHz computer.

Good fun

Matt
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Old 2022-02-22, 04:51   #13
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

32·131 Posts
Default Matt's factordb.com session tonight

I know you all are eager to see this.
For a laugh, see reddit.com/r/softwaregore

This is code gore.

# My comments were lost in translation, so you see "NULL".
Code:
> NULL;
> ifactor((2^303-26070)*(1/14318710184332826954770562));
%;
Warning,  computation interrupted
> NULL;
> NULL;
> ifactor((2^303-12364)*(1/17111387030591077765288038823334466452));

        (421924499807849134091) (2257193170479512364241080475925467)
> NULL;
> 
> ifactor((47^47-607868*3^151)*(1/563876793527));

  (320053816119330053) (17749185239857015560248112454200033855665554126457)
> NULL;
# that was 84 seconds of my computation time.
Factordb.com wants these factorization s, and I have a tool that can do it, so I help out.

Have a pleasant rest of your day.
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Old 2022-02-22, 08:37   #14
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

117910 Posts
Default More factordb.com

Hi again all,

Code:
> ifactor(12728090287417836575217719014652994601005209080166443917625601931139);
(23) (71) (79) (97) (101) (103) (127) (131) (157) (251) (307) (311) (331) (449) 

  (523) (661) (881) (937) (9511) (1831) (2371) (18691) (7561) (2731) (2311)
> ifactor(83960497724513525996447551);
        (103) (137) (223) (271) (397) (433) (449) (853) (1153) (1297)
> ifactor((47^47-607615*3^151)*(1/5888921458));
(3742690805057637823137877) (4695287137889797061) (30955787507078026189588333)
> ifactor((2^303-13794)*(1/468401961602));
(270404512589470744637168966897) (1286637028865374347491025669817071695141439\

  61165631)
> ifactor((2^303-28584)*(1/16450495022145781578813822166184));

     (34855869486345119430765739853) (28420636125756948420304044911387)
The last one is a C60 that splits into a P29 and a P32.
The above code represents 10 minutes of my computer's calculation time.
Good fun.
Matthew

Last fiddled with by MattcAnderson on 2022-02-22 at 08:38 Reason: clean up code
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Old 2022-02-22, 08:45   #15
kar_bon
 
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Mar 2006
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Default

Please try yafu, for such small numbers, it only needs a few seconds to calculate the factorization.
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Old 2022-02-22, 13:48   #16
EdH
 
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Dec 2009
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Default

Or, even PARI/GP (available in most linux repositories):
Code:
$ date;echo "factor((2^303-28584)*(1/16450495022145781578813822166184))" | gp -q;date
Tue Feb 22 08:31:59 AM EST 2022

[   34855869486345119430765739853 1]

[28420636125756948420304044911387 1]

Tue Feb 22 08:32:09 AM EST 2022
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Old 2022-02-22, 23:17   #17
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default

I appreciate the suggestions, kar_bon and EdH.
For some reason, I prefer Maple, under a Windows platform.
It is easier for me to use.

At least you looked at my blog. You both get an A+.

I am an ex school teacher, at community college level. Now retired.

Regards,
Matt

Last fiddled with by MattcAnderson on 2022-05-30 at 02:23 Reason: spelling error
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Old 2022-05-29, 10:28   #18
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default

I did 3 factorizations tonight. I used Maple and it took 242 seconds. I know yafu is faster.
The composite numbers have 71 digits so 3 separate C71.

> ifactor((10^77-902097)*(1/4617559));
(1231835793096446867189849001929203) (17580641889876672351849523974116725939)
> ifactor((10^77-903192)*(1/2421224));
(44153726497395743090944141784629739) (935400648594425033776747820595443203)
> ifactor((10^77-903567)*(1/7043737));
(18356243707875186787152019) (773415823472806954251581178472905383713563811)
>

Regards,
Matt
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Old 2022-05-30, 09:39   #19
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Default

I tried, unsuccessfully, to download yafu on my Windows computer. So I used Maple again.

850 seconds of computer time to do the 10 factorizations. So that's 14 minutes. plus the time it took me to cut and paste the numbers.

> ifactor((10^79-71467)*(1/100516407));
(415196520508633322410371037) (239612427241508060164162583566211246413160687)
> NULL;
> ifactor((10^79-58711)*(1/169197177));
(32217712123101751) (3322354389083) (552161643662521620096524754679840484591029

)
> NULL;
> ifactor((10^79-59127)*(1/134535283));
(10246441372319107150610777) (7254220359728226675028355218499318580974208203)
> NULL;
> ifactor((10^79-65147)*(1/746381351));
(786033472688938268962583638913) (17045046085811117653716230646110641196531)
> NULL;
> ifactor((10^79-88336)*(1/692835696));
(365851341700473666376338158849) (39451642843514306648014973762393822230441)
> NULL;
> ifactor((10^79-147445)*(1/277265805));
(92090012999657744473389857339) (391643708323158726317940739521054443982709)
> NULL;
> ifactor((10^79-193190)*(1/336498370));
(614639931266729357953) (48349976078148992975842315467923320911055809375821)
> NULL;
> ifactor((10^79-213027)*(1/247638251));
(455493389572979327) (191729565517439161) (462392845009718659471979432536148209

)
> NULL;
> ifactor((10^79-217011)*(1/177863789));
(4171142998968471594400629914883503) (13478990935094332180998014639659382767)
> NULL;
> ifactor((10^79-294977)*(1/694650499));
(98291098940387286868762339) (146460144157043485287961013347211563879071143)
> NULL;
>
All these composite numbers were 71 digits. I typed out the length of the prime factors, but it was
lost in the cut and paste. You only see NULL;

Have a nice day.
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Old 2022-07-02, 00:20   #20
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

32·131 Posts
Thumbs up

This is it.
Good times
Look




58375189765560121426618297669679<32>
Factor already known
Found 2 factors and 0 ECM/P+1/P+1 results.
Thank you for your contribution!!
Result:
status (?) digits number
FF
fully factored

74 digits


1104285714...57<74>
=
741005168702867771<18> ·
255288887770650551262373<24> ·
58375189765560121426618297669679<32>

New calculation - the story so far (star wars reference)
3964156213...71<74> factors as 76369348944813067995542418601892989907<38> times 1656496193897081<16> times 313358319590708066713<21> times 76369348944813067995542418601892989907<38>.

Last fiddled with by MattcAnderson on 2022-07-08 at 05:03
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Old 2022-07-20, 17:14   #21
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

32·131 Posts
Smile today's factordb session

Today I learned that
(10^79-253653)*(1/63408193995913273) <63>
equals
1240407261075014928350683*127142374043023096518690934457531891833

in other words, we start with a Composite number (C) and find its prime factors.
note that C63 means a positive composite whole number with 63 digits.
a C63 equals a P25 times a P39.
This is full prime factorization.
A P39 is a 39 digit prime whole number, non-negative.
I did the calculation that factordb.com asked for using Maple software.
Got this message "Thank you for your contribution!!"

similarly,
(10^85-61574)/23838143056604878950854
equals
30957322240919310023385302747079353*(221309510703443*61229979274861)

So this C63 equals a P35 * a P15 * a P14.
Again, fully factored (FF)
And a second "Thank you for your contribution!!"
It makes me feel like I am doing something earth shattering :--)

Now, to continue the exercise,
(47^47-3^151*625186)/15013167471079231
and we have two nice little prime factors
10159422641338012069*20875181318585948571976024569935102678851739
So we see that C63=P20*P44.
And our third "Thank you for your contribution!!" from factordb.com

Having fun, I continue,
(10^82+18525)/29418038266886705275
equals
1144138865405169632908059167*(34751873131457214461*8549275942075213)
we have a C63 that is represented by 3 nice prime factors,
A P28, a P20 and a P16.
These calculations take about 20 seconds apiece on my rig.
And of course, we see "Thank you for your contribution!!".

Proceeding,
(10^91+204520)/25623583168219463536366822120
equals
767341649510268970050796643*508594158619368915079248811240051147
This is summarized as a C63=P27*P36
and, of course, the kudos, "Thank you for your contribution!!"

More,
(10^79-338439)/57630465867129883
equals
10078773747059137326876880513*17216313947893011808535210545803259
Sumarized as C63=P29*P35

Last one for today,
(10^77-188202)/388369050029614
equals
13224258579233485913*(10179633027616307963321489*1912722349862568901)
So, another C63 is 'friable' as P20 * P26 * P19.
I read about 'friable numbers' in an academic paper. According to Google, it means 'easily crumbled'. As in, the soil was friable between her fingers. At first, I thought it meant fryable, like can be cooked, like an egg is fryable. But the spelling is different. Composite numbers are friable into primes, with the right tool.

7 calculations with 119 seconds of computer 'calculating' time.

Good fun.
Have a nice day.
Matt
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Last fiddled with by MattcAnderson on 2022-07-20 at 17:37
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Old 2022-11-04, 06:32   #22
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

32·131 Posts
Smile more factordb.com exercises

Hi all, thought I would document some excercises for factordb.com tonight.
These are composite numbers without known factors,
that is, until I find those factors. Seems like an unending quest for more integers.

1)
1023158077...47<65>
= 42251827687945340008871<23> · 242157116825950976029865397595040631876557<42>

that is
10231580773539729820091760424032485047135317471837448839756937147<65>
now has its full prime number factorization.
23 seconds for Maple calculation

2)
2177776163...77<65>
= 3183065695484865379709731<25> · 6841756883316582905918167565310671762767<40>
so
21777761632132463921562492356618166667408889079359127924553385677<65>
is a friable (composite) number.

3)
2203644330...59<65>
= 318901290004477973928655822387<30> · 69101141942505843993250048862248057<35>
similarly,
22036443306247652594045078394976506803452505721647364050927852059<65>
has two prime factors.

Have a nice day.
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