20141211, 18:04  #1 
Apr 2012
Brady
2×3^{3}×7 Posts 
Primality question.
I came across a reference to 1 considered prime years ago.
http://mathforum.org/kb/message.jspa?messageID=1093172 Is there any theoretical utility in considering this number as such? 
20141211, 18:12  #2  
Nov 2003
16444_{8} Posts 
Quote:


20141211, 19:25  #3 
Apr 2012
Brady
2×3^{3}×7 Posts 
Good pun and thank you for the reply.
My reason for posting is that all primes can be developed from (1,7,11,13,17,19,23 +30*n) where 2,3,5 are not included. Riesel's 1984? book notes this in the initial first or second chapters. The sum of digits of every prime is one of 1,4,2,8,5,7 which is the cyclic reciprocal of 7 ( I have not found a proof of this and pointer would be appreciated). To me, this is a curiosity but an interesting one. Last fiddled with by jwaltos on 20141211 at 19:28 
20141211, 19:38  #4  
May 2013
East. Always East.
3277_{8} Posts 
Quote:
That leaves a sum of 0 (mod 10, I imagine). 19 is a counter example of that, so I'm not sure why it was missed. 

20141211, 21:42  #5 
Apr 2012
Brady
101111010_{2} Posts 
Thanks Mawn.
Last fiddled with by jwaltos on 20141211 at 22:30 
20141211, 22:36  #6 
Jun 2014
120_{10} Posts 

20141212, 00:50  #7  
May 2013
East. Always East.
11×157 Posts 
Quote:
"4 measures 12" as in if you have 12 blocks, you could measure them if you had a stick that was 4 blocks long. 

20141212, 03:14  #8 
Jun 2003
7·709 Posts 

20141212, 04:39  #9  
May 2013
East. Always East.
3277_{8} Posts 
Quote:
The thing about the 3 still holds then, @OP. If a number's digits add up to something bigger than 9 and still a product of 3, it eventually decomposes back to 3 6 or 9. 396  > 18 > 9. 1299 > 21 > 3. Etc 

20141212, 17:22  #10 
Feb 2006
Denmark
2·5·23 Posts 
You are missing 1, and it's more common to use 29 than 1. The usual form is (1,7,11,13,17,19,23,29 + 30*n). In case you don't know, 30 = 2*3*5 (product of the first three primes), and 1,7,11,13,17,19,23,29 are the numbers below 30 and coprime to 30, so (1,7,11,13,17,19,23,29 + 30*n) is simply the numbers with no prime factor <=5. Its' trivial to make similar expressions for numbers with no prime factor <= p for other small primes p. p=2 gives that all primes above 2 are odd (2n+1). p=3 gives that all primes above 3 are of form 6n+1 or 6n+5, but in this case it's more common to use 1 in 6n+/1. p=7 is also relatively easy by hand. After that I recommend using a computer (it's a trivial programming exercise, please don't post the long lists of coprime numbers).

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