20210615, 07:34  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×3×151 Posts 
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) 64bit 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. 
20210615, 07:57  #2 
"Matthew Anderson"
Dec 2010
Oregon, USA
1612_{8} Posts 
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 20210615 at 08:26 Reason: added link and gave more details 
20210615, 08:29  #3 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×3×151 Posts 
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 
20210615, 16:57  #4 
"Matthew Anderson"
Dec 2010
Oregon, USA
2·3·151 Posts 
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 Last fiddled with by MattcAnderson on 20210621 at 03:48 Reason: 6th calculation 
20210615, 18:20  #5 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
23431_{8} Posts 
Maybe you should gather your work up for 1 week and then post your results. Posting minor updates frequently is tiresome.

20210817, 04:20  #6 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×3×151 Posts 
Hi all,
I have been doing several requested integer factorizations for factordb.com. Some composites are semiprimes, 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 10,000smooth and have many factors. Those numbers take much less computation time Still fun. Matt 
20210923, 10:34  #7 
"Matthew Anderson"
Dec 2010
Oregon, USA
2×3×151 Posts 
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, (2123766^171)/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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