20200715, 22:41  #23  
Nov 2016
4747_{8} Posts 
Quote:
Last fiddled with by Uncwilly on 20200716 at 14:01 Reason: TRIM YOUR QUOTES 

20200811, 22:38  #24  
Jan 2020
3·41 Posts 
Quote:
You should never have the "3" in base 3 because there are only [0, 1, 2]. I used my color balls and I figured the answer out without using the base calculator. Last fiddled with by tuckerkao on 20200811 at 23:16 

20201007, 11:02  #25 
"Ruben"
Oct 2020
Nederland
2×19 Posts 
Numbers ending in 0

20201007, 11:12  #26 
"Ruben"
Oct 2020
Nederland
2·19 Posts 
Base 30
I think base 30 might be interesting, primes (other than 2, 3 and 5) would only end by :"1, 7, B, D, H, J, N, T"

20201007, 11:35  #27 
Sep 2006
Brussels, Belgium
7×233 Posts 
.
Last fiddled with by S485122 on 20201007 at 11:36 Reason: Why state the obvious ? 
20201018, 10:19  #28  
Jan 2020
3×41 Posts 
Quote:
12 is a prime 22 is a composite 102 is a prime 112 is a composite 122 is a prime Add all the digits together as in the decimal base, it should reveal whether the numbers are even or odd in base 3. Quote:
Last fiddled with by tuckerkao on 20201018 at 10:44 

20201018, 10:25  #29  
Nov 2016
100111100111_{2} Posts 
Quote:
https://primes.utm.edu/glossary/page...t=MinimalPrime In 1996, Jeffrey Shallit [Shallit96] suggested that we view prime numbers as strings of digits. He then used concepts from formal language theory to define an interesting set of primes called the minimal primes: A string a is a subsequence of another string b, if a can be obtained from b by deleting zero or more of the characters in b. For example, 514 is a substring of 251664. The empty string is a subsequence of every string. Two strings a and b are comparable if either a is a substring of b, or b is a substring of a. A surprising result from formal language theory is that every set of pairwise incomparable strings is finite [Lothaire83]. This means that from any set of strings we can find its minimal elements. A string a in a set of strings S is minimal if whenever b (an element of S) is a substring of a, we have b = a. This set must be finite! For example, if our set is the set of prime numbers (written in radix 10), then we get the set {2, 3, 5, 7, 11, 19, 41, 61, 89, 409, 449, 499, 881, 991, 6469, 6949, 9001, 9049, 9649, 9949, 60649, 666649, 946669, 60000049, 66000049, 66600049}, and if our set is the set of composite numbers (written in radix 10), then we get the set {4, 6, 8, 9, 10, 12, 15, 20, 21, 22, 25, 27, 30, 32, 33, 35, 50, 51, 52, 55, 57, 70, 72, 75, 77, 111, 117, 171, 371, 711, 713, 731} Besides, if our set is the set of prime numbers written in radix b, then we get these sets: Code:
b, we get the set 2: {10, 11} 3: {2, 10, 111} 4: {2, 3, 11} 5: {2, 3, 10, 111, 401, 414, 14444, 44441} 6: {2, 3, 5, 11, 4401, 4441, 40041} Now, let's consider: if our set is the set of prime numbers >= b written in radix b (i.e. the prime numbers with at least two digits in radix b), then we get the sets: Code:
b, we get the set 2: {10, 11} 3: {10, 12, 21, 111} 4: {11, 13, 23, 31, 221} 5: {10, 12, 21, 23, 32, 34, 43, 111, 131, 133, 313, 401, 414, 14444, 30301, 33001, 33331, 44441, 300031} 6: {11, 15, 21, 25, 31, 35, 45, 51, 4401, 4441, 40041} 7: {10, 14, 16, 23, 25, 32, 41, 43, 52, 56, 61, 65, 113, 115, 131, 133, 155, 212, 221, 304, 313, 335, 344, 346, 364, 445, 515, 533, 535, 544, 551, 553, 1112, 1211, 1222, 2111, 3031, 3055, 3334, 3503, 3505, 3545, 4504, 4555, 5011, 5455, 5545, 5554, 6034, 6634, 11111, 30011, 31111, 33001, 33311, 35555, 40054, 300053, 33333301} 8: {13, 15, 21, 23, 27, 35, 37, 45, 51, 53, 57, 65, 73, 75, 107, 111, 117, 141, 147, 161, 177, 225, 255, 301, 343, 361, 401, 407, 417, 431, 433, 463, 467, 471, 631, 643, 661, 667, 701, 711, 717, 747, 767, 3331, 3411, 4043, 4443, 4611, 5205, 6007, 6101, 6441, 6477, 6707, 6777, 7461, 7641, 47777, 60171, 60411, 60741, 444641, 500025, 505525, 3344441, 4444477, 5500525, 5550525, 55555025, 444444441, 744444441} Can someone complete my base 7 and 8 set? Also find the sets of bases 9 to 36. 

20201018, 10:31  #30  
Jan 2020
173_{8} Posts 
Quote:
In base 8, the "13" is a prime as it's called 1 Octa 3. It's quiet easy when I use my color balls to figure out the primes in the alternative bases up to several hundreds. I highlight the primes with the black stones in the decimal base first, then change the width of the arrays to 7 or 8, then I get the primes for base 7 or base 8. There are also different scales derived from the alternative bases from length to weight to volume and so on  http://www.dozenal.org/drupal/sites_...al_arith_0.pdf Maybe there needs to be a subforum for the numbers and calculations in the different bases as most members don't understand what we are talking about. Last fiddled with by tuckerkao on 20201018 at 11:25 

20201019, 05:36  #31 
Romulan Interpreter
Jun 2011
Thailand
8,963 Posts 
As somebody pointed to me on PM, this is insulting for the most members of this forum, who are better qualified than you, to talk about the subject. Of course we understand numeration bases. But what you are doing with them, is called "mess". I think a week holiday may make you reevaluate your priorities...

20201023, 13:53  #32 
"Ruben"
Oct 2020
Nederland
2·19 Posts 
Efficient bases for finding primes
I noticed that if we classify the bases according to how efficient they are to identify at once (by the last digit) composites, base 10 is "quite" good, but not the best!
Not even up to 10, as base 6 is better. I saw above that some wish a shifting to base 12, which is better than 10, but it's on the same rank as 6. If we want to change our number system, as we already have existing bases, why not change for an even more efficient, how about 30, (I don't know if we have enough symbols for base 210). 
20201023, 15:30  #33 
Jun 2003
2×5×479 Posts 
You're thinking like a human. For a computer, what you just said is a nanosecond of computation (to divide by the base and check the remainder). This brings no efficiency to prime finding.

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