Heh...cheers, though in retrospect I think I'm asking a bit too much in this particular problem, and the first number in the sequence can be argued that it doesn't belong with the standard definition of prime numbers (ie: 1 isn't a prime)

There is a skill to setting a good puzzle that I have yet to acquire!

Originally posted by Agerg Heh...cheers, though in retrospect I think I'm asking a bit too much in this particular problem, and the first number in the sequence can be argued that it doesn't belong with the standard definition of prime numbers (ie: 1 isn't a prime)

There is a skill to setting a good puzzle that I have yet to acquire!

No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

Originally posted by telecomladyj No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

If we let 1 be prime we lose the unique factorisation of the integers (up to ordering that is). No longer can we say 12 = 2 x 2 x 3, since we can also factorise it as
1 x 1 x 1 x 2 x 2 x 3 or
1 x 2 x 2 x 3 or
.
.
.
1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 2 x 2 x 3
ðŸ˜µ

Originally posted by telecomladyj No no, I think you have a good point.
I have long argued that 1 should be considered prime, since the definition of a prime is that it "can only be divided by itself and 1" just because itself IS 1 shouldn't preclude it from being considered prime--- says I!

A non-prime is a number composed of two or more primes. Like 6=3x2. Right?
So if 1 is a prime, then 5 is a non-prime, because 5=5x1.

By including 1 in the set of primes, then you have to exclude 1 every time you want to have a unique factorization. Very impractical.