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Old 2021-06-15, 07:34   #1
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

90610 Posts
Thumbs up fun with factordb.com

Tonight I found that a C75 is a P32 times a P44.

It required 165.14 seconds of computer time,
Using Maple 13 student version
and my computer is
Windows 7 Home Premium, service pack 1
(stable but fighting update suggestions)
Dell Studio XPS 8100
Intel(R) Core(TM) i7 CPU 870 @ 2.93GHz
(not overclocked not dusty no current heat issues)
8.00 GB Installed memory (RAM)
64-bit Operating System
(no kids in the house, have wife and dog (Annabel - see pets post for picture))
(possible roommate in future. Paying tenant. Want more vacation and
restaurant meals. )

anyway enough with the personal part. Here is the exciting -

Before I added data, the C75 was determined composite and was
definitely not of unknown character (prime or composite).

C75

754774190053185247280130362209008682706014273561997303388021674990481034789


P32 and P44

48513722976304242000153731071441<32> · 15557952343130679147755701144328513488043029<44>

Going to eat now.
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Old 2021-06-15, 07:57   #2
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

2·3·151 Posts
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Found a C70

5251595955542976485924773357619648101146114174676995076345134370657229

away from keyboard

3721001974321543266672687967*(22424797223486196447937965793*62936542414259)

P14 * P28 * P29

62936542414259<14> · 3721001974321543266672687967<28> · 22424797223486196447937965793<29>

Did this before, some years ago when I was working on Prime Constelations.
Originall calculations for our online encyclopedia of integer sequences dot org

https://sites.google.com/site/primeconstellations/


This website is in the style of wikipedia and is owned by google so I can no longer make changes to it.

However, I have backed it up, on little Universal Serial Bus (USB) memory storage device
(thumbnail hardware)

Good fun

Last fiddled with by MattcAnderson on 2021-06-15 at 08:26 Reason: added link and gave more details
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Old 2021-06-15, 08:29   #3
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Now a C67

2878189567560747844730239605664433489522492631397317607235068302073

so interesting

and useful in at least 3 millennia as we continue to colonize Mars.

good mathematical trivia

away from keyboard again
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Old 2021-06-15, 16:57   #4
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Now an previously unknown C83 is a P36 times a P48

To show

38146669211999441488164746438552634539130258479280936639266759628326547189425577797<83>

134954146509066228002222828521591151<36> · 282663928443552831960531852882219045579470788747<48>

As usual, Maple computer algebra system does the calculation.

A second calculation, where I used my computing power for the common good.

27574716087185233327163536636771065444982198463691038366730762645413521090022448847
is
75447098840450044005713687
times
365484114180430021057030446268054759428025435631091644681

So a C83 is a P57 times a P26


Two calculations for the price of one.

Now a third calculation
# a C72 needing factoring
>
> ifactor(431951947630596321658466238929565258017885765694269056314003364436248649);
print(`output redirected...`);
# input placeholder
(232353028381758099222878389962317) (1859033000942408277227568406797114146797)

# calculation number 4
# an easy C72
> ifactor(165899983662255688471809882590614582299651829639766394486046093934534531);


(23024954280605621537)
(5039842424514739352289733)
(1429652897234526894170944711)

That is P20 * P25 * P28

# C63 needs factorization
> ifactor(138152297859254560882099296463904468254265421713121317806141139);

(3355920492373395691681335541) (41166737463899093611930167715437479)



and only a few tens of seconds of computer time.

another one
# C63 factored and reported to factordb.com
> ifactor(189538484332123294045600201844861506643780749140978223831637939);
print(`output redirected...`); # input placeholder
(143820796667507966711791845013) (1317879532890557820822643382123303)

# only 20 seconds of computation time on this one.

another one
# C60 factored and reported to factordb.com
> ifactor(151996640445840293245405079864773923954627764256609641566429);
print(`output redirected...`); # input placeholder
(24285925367577446693795141) (6258630797274913966996966660483769)

this C60 factored in under 7 seconds of computation time.

another one
61493390605085032632697975887667162345441<41> = 1103526119<10> · 55724454135086070067633782837239<32>
this includes the digit count at the end of the numbers.
less than a minute of computation time. Awesome.

another one
# a C74 factored and reported to factordb.com
# 131 second computation time on this one
> ifactor(24582591584604460062256786284620852944170003807267337840218983547251269109);

(35183656999490713445063) (698693475353067910344746424750961346480505668287843)
so we see C74 = P23*P51.
totally awesome


another one
# C80 factored and reported to factordb.com
ifactor(72932186055774864363694027742904983348521837335186626460219369612723227742902833);

(32107229549154428393930171)*
(2271519127619517593683308004402503075736300288979505923)

another one A C25 factors into a P17 and a P9. Specifically,
> ifactor(4061175182312812557675533);

(359831579) (11286322322235127)
And factordb.com database and website did not know this answer until I told it.
It took less than a second of computation time.

another one, a C68 is fully factored with a P21 and a P47
> ifactor(29033656705936299898290356598350209400998240054447587486839502132031);

(751343048685549742241) (38642344208454099899513077332898081508596404191)
calculated in 42 seconds of computer calculation.
Factordb.com did not know this result until I told it.
That database is gaining data.

pretty quick

here is another one. A C76 that was factored by my computer in 1 minute and 58 seconds, quick.

5331122349339808366392915411117415062120156657223201132434071632497915360917

= 171206516971178333556612731<27> * 31138548015886995766862127463540612963975610677807<50>

To be sure, a C76 = P27 * P50.

another one
A C61 factors as a P19, a P20, and a P23.
Note that
19 + 20 + 23 = 62, which is very close to 61.
specifically
9011824145847925227992399064278238744957209982537661572099487
= 2305728636742600703<19> · 65204944046653124213<20> · 59941000602693444703933<23>.

It is interesting to consider numbers near a googol. A googol is a number with 101 digits.
Factorize!
10^100+91<101> = 79 · 6880726549933<13> · 5068013823241573808081<22> · 154972061606042703135868972981<30> · 23423263752533621617530706402640533<35>
very interesting

here is another one
> ifactor(72087326271153459481230176223024266382449693517548185641957020283436256653774674334563461);

(126099801428594826245322089) (571668832579197769805225819739758331955032068099267073705909949)

So a C89 is a P27 times a P63 in disguise :--)
This calculation took less than 66 minutes with my Maple tool.

fun

see attached - Maple to factor integers.pdf
Lots of fun.

Matt
Attached Files
File Type: pdf Maple to factor integers.pdf (126.5 KB, 39 views)

Last fiddled with by MattcAnderson on 2021-06-21 at 03:48 Reason: 6th calculation
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Old 2021-06-15, 18:20   #5
Uncwilly
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Maybe you should gather your work up for 1 week and then post your results. Posting minor updates frequently is tiresome.
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Old 2021-08-17, 04:20   #6
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

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Hi all,

I have been doing several requested integer factorizations for factordb.com.

Some composites are semi-primes, that is of the form composite = prime1 * prime2.

My last one was

(10^71+33123)/14219691071<61> = 12684852287106422167790489<26> · 554401535483277901401800643095782117<36>

Sometimes the numbers are 10,000-smooth and have many factors.
Those numbers take much less computation time


Still fun.

Matt
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Old 2021-09-23, 10:34   #7
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

2×3×151 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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