June 17th, 2017, 10:49 AM  #1 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0  question on odd numbered composites
Has anyone ever noticed that the odd numbered composites start as "3*Prime" and work up through the other Primes in order? (ex.: 3*3,3*5,3*7,etc.; 5*3,5*5,5*7,etc. and so on.)

June 17th, 2017, 12:26 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,478 Thanks: 1314 
How do those lists continue?

June 17th, 2017, 12:30 PM  #3 
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342  
June 17th, 2017, 01:02 PM  #4 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
They continue up through the primes (3*prime and 3*composite). I ignored the composites, as there were already composites.
Last edited by skipjack; June 17th, 2017 at 04:09 PM. 
June 17th, 2017, 01:09 PM  #5 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
Yes, 3*composite also starts the string for the composites. I left out the composites thinking that everyone would understand those numbers were already composites. Please forgive me for forgetting to not keep to the basics.

June 17th, 2017, 01:25 PM  #6 
Senior Member Joined: Aug 2012 Posts: 1,414 Thanks: 342  Can you explain what you are doing? For example 105 = 3*5*7 is less than, say, 17*47. So your initial claim that you generate the odd composites "in order" (your words) by first taking all the odd semprimes (products of two odd primes) is wrong.

June 17th, 2017, 01:30 PM  #7  
Senior Member Joined: May 2016 From: USA Posts: 679 Thanks: 283  Quote:
$5 \text { is 2nd odd prime}$ $7 \text { is 3rd odd prime}$ $9 = 3 * 3 = \text { 1st odd composite } = 3 \times \text {1st odd prime}$ $11 \text { is 4th odd prime}$ $13 \text { is 5th odd prime}$ $15 = 3 * 5 = \text { 2nd odd composite } = 3 \times \text {2nd odd prime}$ $17 \text { is 6th odd prime}$ $19 \text { is 7th odd prime}$ $21 = 3 * 7 = \text { 3rd odd composite } = 3 \times \text {3rd odd prime}$ $23 \text { is 8th odd prime}$ $25 \ne 3 * 11 \implies \text {4th odd composite} \ne 3 \times \text {4th odd prime}$ It falls apart on the fourth example. Reminds me of the old joke. 3 is prime. 5 is prime. 7 is prime. By induction, 9 is prime. EDIT: Perhaps the OP was trying to say something different that is valid, but, in that case, I have no clue what he was trying to say. Last edited by JeffM1; June 17th, 2017 at 01:36 PM.  
June 17th, 2017, 01:34 PM  #8 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
True. But to get to 17*47, or any other composite on a sieve, the string always starts at 3*p or c.

June 17th, 2017, 01:38 PM  #9 
Senior Member Joined: May 2016 From: USA Posts: 679 Thanks: 283  
June 18th, 2017, 12:24 PM  #10 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
I am talking about an infinite number of strings. The first string is the 3*P or C string. The first 3 composite string starts at 3*3=9, and moves up through the composites and primes. The strong of 5*p or c composites doesn't start at 5*5=25. It starts at 5*3 nd moves up. Same with the 7*p or c string. Same with any p*p or c string imaginable. True, this is useless, but I thought it for general discussion , as the name of this forum implies , and was wondering if it had been noted any where before.
Last edited by KenE; June 18th, 2017 at 12:28 PM. 

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