# Talk:Senary

## hands

What does:

Base 6 can be counted on hands by using each hand as a digit (0 to 5).

mean? I assume the second 'hand' is a mistake. Tompagenet 10:33, 5 Aug 2003 (UTC)

It was probably a presumption that you count 1-6 instead of 0-5... Dysprosia 10:34, 5 Aug 2003 (UTC)
What is probably meant is: Take your right hand, close it. This is "0". Open one finger, this is "1", etc. Open all five fingers, this is "5". So on one hand you can handle one "senary digit". With two hands you can count from 0 to 35 (= 55(6)). --SirJective 12:04, 21 Nov 2003 (UTC)
This is precisely what I meant Karl Palmen 15:23, 21 Nov 2003 UT

## prime numbers

So this article implies, if p is prime, then p mod6 = 1 or p mod 6 = 5 ... can we get a link to an article or reference for this? linas 01:10, 1 Apr 2005 (UTC)

Dohh, never mind, its obvious. linas 00:38, 10 August 2005 (UTC)

## errors

All prime numbers besides 2 and 3 end in either 1 or 5. Did the definition of Prime Number change? What happened to only being divisible by 1 or itself? What about 13, 17, 19, 23, 29, 37, 43, 47, 53, 59, 67, 73, 79, 83, 89, 97, 103, 107, 109, 113, ...? malachid69 08:14, 9 Aug 2005 (UTC)

That's base 10 not base 6. The statement is that p mod 6 is congruent to 1 or 5. The article wording should be changed to say "congruent" exactly in order to avoid this confusion. linas 00:38, 10 August 2005 (UTC)

## big errors

There is a big mistake in this page. No number ending in 5 (except for 5 itself) is a prime number. Every single number with 5 as the final digit can be devided by 5. A correct list of prime numbers would be 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, etc.

I also noticed that there are quite some known perfect numbers that don't have 44 as the final two digits, like 28, 496 and 8128.

I don't know who wrote this page, but his maths are worse than mine, and people should not try to write articles about things they don't know about.

I am not great at maths, so I have no idea how I should correct this error and I don't have a clue what Senary would be good for, but I just thought I'd write this down here so someone who does know can correct the error here and then delete my message.

(The above message was posted on the main article page by . I'm just moving it here. - ulayiti (talk) 12:00, 20 August 2005 (UTC))

The poster didn't have a clue. However, everyone who reads this article seems to trip over this, so I will try to fix the article in just a moment. linas 15:56, 20 August 2005 (UTC)
OK, I think I fixed it for good. linas 16:15, 20 August 2005 (UTC)

## consistency errors

I was looking through the other numeral systems, and I saw the box on the right that had all of the numeral systems in a single easy-to-use box, I would put it in myself, but i don't know how... example: Unary numeral system 18:37, 26 August 2005

## Confusion

This entry is almost incomprehensible for a layman. As a layman who knows nothing about numbers and number systems, maybe someone could edit this so that someone who doesn't know what base 6 is could understand it? Isn't that the point of Wikipedia? This entry is useless to someone with limited knowledge of math terminology, symbology. —The preceding unsigned comment was added by 131.96.28.51 (talk) 00:58, 27 April 2007 (UTC).

A layman could click on numeral system or base early in the article to get information necessary for understanding the article. Karl 10:03, 27 April 2007 (UTC)

## "Furthermore, all known perfect numbers besides 6 itself have 44 as the final two digits"

This means nothing. Every number (2n-1)2n-1 with n = odd number > 2 has 44 as the final digits in base 6. The even perfect numbers are only a part of these numbers. --Zumthie (talk) 23:46, 10 December 2008 (UTC)

So does every power of 10 besides ten itself. I disagree that such an argument makes the statement meaningless. Which other bases have all known perfect numbers besides 6 ending with the same two digits? Karl (talk) 11:33, 12 December 2008 (UTC)

See base 2:
 base 2 base 10 even perfect numbers 110 11100 111110000 1111111000000 1111111111111000000000000 111111111111111110000000000000000 1111111111111111111000000000000000000 … (22-1)21 (23-1)22 (25-1)24 (27-1)26 (213-1)212 (217-1)216 (219-1)218 … 6 28 496 8128 33550336 8589869056 137438691328 … In base 2 the first part of an even perfect number is a Mersenne prime, digits 1, the rest of the digits are 0.

--Zumthie (talk) 23:00, 12 December 2008 (UTC)

## 55 base 6

556 ends in a 5 but is 3510 which is certainly not a prime number.

70.171.113.214 (talk) 13:31, 15 March 2010 (UTC)

All primes end in 1 or 5, not all numbers ending in 1 or 5 are prime. — sligocki (talk) 04:03, 17 March 2010 (UTC)

## proof

Just wondering who proved that all prime numbers end in 1 or 5 when written in base 6 (or whether it is proved). The article states it without any sources or proof. A citation would also be useful for the claim that all known perfect numbers (when written in senary) end in 44. 122.107.15.145 (talk) 11:18, 31 March 2010 (UTC)

It is analogous to the reason that no prime numbers in decimal end in 2, 4, 5, 6, 8. Here's a proof: any number in base 6 is of the form $x = a_0 + a_1 * 6 + a_2 * 6^2 + a_3 * 6^3 + ... = a_0 + 6 * (a_1 + a_2 * 6 + a_3 * 6^2 + ...) = a_0 + 6k$, where k is an integer (here $a_n$ are the senary digits). Thus if $a_0$ is divisible by 2 or 3, then $x = a_0 + 6k$ is divisible by 2 or 3. 1 and 5 are the only senary digits that are not divisible by 2 or 3, so all primes (other than 2 and 3) have last senary digit 1 or 5. Cheers, — sligocki (talk) 01:22, 1 April 2010 (UTC)
It is well known, that all even perfact numbers are the product of a Mersenne prime and half of one plus that Mersenne prime. The powers of four besides 1 end in either 04 or 24 in senary. This can be proven by induction. Doubling these numbers and subtacting 1, leads to a set of numbers that contains all Mersenne primes besides 3 and they end in 11 or 51 respectively. When the respective numbers are multiplied one always get a number ending in 44. 44 is an automorphic number in senary just as 76 is in decimal. Karl (talk) 12:14, 1 April 2010 (UTC)
Thanks. The proof should be included in the article though. 122.107.15.145 (talk) 12:35, 13 April 2010 (UTC)