## Re: [PrimeNumbers] A New Kind of Prime Number

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• ... - Suppose that n is a first order prime. Then n-1 is either prime, or a power of 2. - Suppose n is a 2nd order prime. Then n-2 is either prime, or a
Message 1 of 3 , Sep 29, 2003
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> I introduce the concept of higher order primes. Zero order primes
> are just the familiar primes; 2,3,5,7 etc. A zero order prime, X,
> if divided by any number less than X and more than one never
> yields a remainder of zero. A first order prime, X, if divided by
> any number less than X?1 and more than 2 never yields remainder
> of
> one. Prime1 numbers are 3, 4, 5, 6, 8, 12, 14 etc. In general, a
> prime Y number ,X, when divided by any number less than X ?
> Y
> and more than Y + 1 never yields a remainder of Y.

- Suppose that n is a first order prime. Then n-1 is either prime, or
a power of 2.
- Suppose n is a 2nd order prime. Then n-2 is either prime, or a product
of powers of 2 and 3 only.
- Do we see a pattern yet? Since 4 is not prime, it follows (I think)
that n is 2nd order iff n+1 is 3rd order.

And so on. My point is, why should the word 'prime' be associated with
these n? I mean, your definition says things about the factorisation of
n-1, or n-2, or whatever, but that doesn't say much about the factors of
n itself.

A sequence of m'th order primes can basically be split into two parts.
One part is a shifted prime sequence, i.e. p+m. The other part is
essentially boring, from a prime point of view, since it is just all
those numbers consisting of prime factors from a finite set.

I don't see anything new in this definition, sorry.

Andy
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