Co-prime number list.

Question

I need to make an infinite sequence of natural numbers which contains no prime numbers, yet any pair of them are co-prime with each other. I tried just finding numbers between 1 - 100 that forms a co-prime list, but couldn't find a pattern or rule that justifies it.

score 1 · Answer 1 · answered Mar 16 '17 at 10:42

1

You could try:

$$\{p^2|p \in primes\}$$

answered Mar 16 '17 at 10:42

JMP

21,771

score 1 · Accepted Answer · answered Mar 16 '17 at 10:44

let $a_n$ be a sequence of natural number such that :

$a_n = p_{2n} p_{2n-1}$ where $p_n$ is the $n$-th prime number surely that $a_n$ contain no prime and every element in the sequence will be co-prime to all other elements in the sequence and there will be infinitely many(Euclid proof).

the sequence starts with $\{6,35,143,323,667,1147,1763,2491,3599,\cdots \}$

Co-prime number list.

2 Answers2