20110917, 23:23  #1 
"Daniel Jackson"
May 2011
14285714285714285714
601 Posts 
Numbers in Other Bases
As shown on the following website, AZ represent 1035, az represent 3661, and 6293 are represented by punctuation (Case Sensitive):
http://home.ccil.org/~remlaps/DispConWeb/index.html Here's an example: 12345ABCabc`~^&*_{94}=403838401633020116561588357495_{10} I used the GIMPS Homepage and found it to be composite (divisible by 2) www.mersenne.org_{94}=23173464146192129623556375950544_{10} Examples of Base36 primes: HEART 101 (Largest known Generalized fermat prime base36) =1297_{10} I found some rules for the last "digit" (base94):
Divisibility rules are also different:
Divisibility Rules for base19:

20110918, 02:08  #2 
Dec 2010
Monticello
5·359 Posts 
Theorem: Numbers can be represented in any base...when you get beyond 16, you need to explicitly state your rules of representation.
Theorem: A number ending in zero in any base representation is composite. 
20110918, 02:38  #3 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5^{2}×229 Posts 

20110918, 04:24  #4 
Aug 2006
3×1,973 Posts 

20110918, 09:21  #5 
Romulan Interpreter
Jun 2011
Thailand
21036_{8} Posts 
Now that is not so clear, you have a number that you can reprezent as ending in 0, no matter what base you choose? :P (this was a joke!)
Or you have a number that ends in 0 when you represent it in "some" base b? In this case, the number is composite if the base is composite, in any case.... not only even bases. Also, if the base is prime, 10 in base b is always prime. Any other number ending with 0 in base b can't be prime (as is divisible by the base), except in case is 10 in base b, and that b is prime itself. by the way, how we can characterize even numbers in a odd base? some fast divisibility criteria? for example in any even base, they end with even "digits" in that base (Mr Silverman will be on my head now for illegal use of the word "digits", sorry! my English is far away to be such good). For example, say, in base 5, any number is even if and only if the sum of the last two digits is even, and I believe that is the fastest way (hope is also true, it just popped up into my head now, did not check it). Any general rule? This just informal, or more than like a curiosity.... Last fiddled with by LaurV on 20110918 at 09:31 
20110918, 13:31  #6 
Dec 2010
Monticello
1795_{10} Posts 
LaurV:
Stand Mr Silverman on *his* head...in that conversation, as in this one, it is very clear from context that we mean a basesomething digit here when we say digit. We're in the lounge, so we can prattle about trivialities, as Mr Silverman might say, as long as we admit that this is (extremely) elementary stuff. Now,to solve your question about evenness, just write your number in arbitrary base out, and keep track of what happens modulo 2. Last fiddled with by Christenson on 20110918 at 13:34 
20110918, 15:32  #7  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:
even even even odd odd even odd even even odd even even odd odd seems to be the pattern for most of the last digits in base 3 but I see it can depend on if the rest of it is an even number. I just looked at base five but I'm not mass generalizing. 

20110918, 17:59  #8 
"Daniel Jackson"
May 2011
14285714285714285714
601 Posts 
Any prime of the form 6x1 is even in base3. "GOD" is part of a prime triplet in base36 (21611, 21613, 21617 in base10). Here's a list of base94 primes with their base10 values shown (Case Sensitive):
Here are some large base36 primes I found: Code:
VELOCIRAPTOR00000000000000000000000000000000000000000000000000000000000000000000000000001 MYTHBUSTERSDDDDDDDDDDDDDDDDDDDDDDDDD MYTHBUSTERSDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDB Last fiddled with by Stargate38 on 20110918 at 18:01 
20110918, 19:16  #9 
Romulan Interpreter
Jun 2011
Thailand
2·11·397 Posts 
This can't be, or I was not clear about "even" numbers. The fact a number finishes in 0,2,4 etc means nothing. These are just symbols. An even number is a number that can evenly be split in 2 parts. For example, 8 is an even number. If I have a heap of 8 coins, I can split thm in two heaps of 4 coins.
In any even base, take 10 for example, is easy to characterize any even number, saying that "a number is even if and only if the last digit of the number is 0, 2, 4, etc", i.e. last digit is an even number. I am used to compute in even bases only, like the most of us (binary, octal, decimal, hex) and I can do fast computing in my mind, even with numbers with many digits (being programmer for more then two decades) in these bases. But it never occur to me till now the fact that if the base is not even, then some even numbers won't end... right. This first pops to my head when I read the original post of this thread. So I asked myself, more like a curiosity, how we would see in a blink of an eye that a number is even, if we would use by default an odd base. We are used to count in base 10, because most probably we have 10 fingers, and that was how our ancestors were counting. How about if they were using the moon phases instead, counting for example in base 7, or so? How we would see in a blink of an eye that a number is even? Same story as we can see (in base 10) that a number is divisible by 3, adding the digits till we got onedigit sum and check if it is 3, 6, or 9 (divisible by 3). I solve this since the last post, but it wasn't as I assumed (about the last two digits). It is a bit more complicated. All of them have to be summed :D Now saying that "in base 3 any prime of the form.... is even" sounds wrong to my ears. The only even prime is 2, and this does not depends of the base you write the numbers in. All other primes are odd. You can't split them in two equal heaps. They wont be primes in this case. Number "12" in base 3 is not even. It is odd. But "112" is even (=14 decimal). And so is "221201011" (= 56226 decimal, even). Last fiddled with by LaurV on 20110918 at 19:40 
20110918, 19:19  #10 
Dec 2010
Monticello
5×359 Posts 
Umm, beyond 16, I can't keep track of which letter corresponds to what value...guess I didn't learn my multiplication tables well enough in school!
I prefer something like: GOD(94) = (16)(24)(13), or spell it all the way out: (16)*94^2 + 24*(94) + 13. Much clearer that way... 
20110918, 19:31  #11  
Dec 2010
Monticello
3403_{8} Posts 
Laurv, let's correct a bit of english here....I think it will help the confusion.
Quote:
As for the statement "in base 3, any prime of the form 6x1 ends in an even digit", I have a small prize for the first NUMBER (prime or not) of the form 6x1 when represented in base 3 that ends in a digit other than 2, assuming the usual conventions of representation for integers. 

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