# question on odd numbered composites

#### KenE

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.)

#### skipjack

Forum Staff
How do those lists continue?

• 1 person

#### Maschke

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.)
How do you account for 3*5*7, etc?

• 1 person

#### KenE

They continue up through the primes (3*prime and 3*composite). I ignored the composites, as there were already composites.

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#### KenE

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.

#### Maschke

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.
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.

• 1 person

#### JeffM1

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.)
$3 \text { is 1st odd prime}$

$5 \text { is 2nd odd prime}$

$7 \text { is 3rd odd prime}$

$9 = 3 * 3 = \text { 1st odd composite } = 3 \times \text {1st odd prime}$

$11 \text { is 4th odd prime}$

$13 \text { is 5th odd prime}$

$15 = 3 * 5 = \text { 2nd odd composite } = 3 \times \text {2nd odd prime}$

$17 \text { is 6th odd prime}$

$19 \text { is 7th odd prime}$

$21 = 3 * 7 = \text { 3rd odd composite } = 3 \times \text {3rd odd prime}$

$23 \text { is 8th odd prime}$

$25 \ne 3 * 11 \implies \text {4th odd composite} \ne 3 \times \text {4th odd prime}$

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.

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#### KenE

True. But to get to 17*47, or any other composite on a sieve, the string always starts at 3*p or c.

#### JeffM1

True. But to get to 17*47, or any other composite on a sieve, the string always starts at 3*p or c.
What string?

#### KenE

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 string of 5*p or c composites doesn't start at 5*5=25. It starts at 5*3 and 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 anywhere before.

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