Is an integer Prime or Composite? Is there any proof an integer being Prime, other than it not being Composite i.e. it has no prime factors? Lists of potentially prime numbers or pseudo primes http://en.wikipedia.org/wiki/Pseudoprime have been identified using a variety of methods. The method below has possibly not been identified before (?)

Many primes can be written in the form, in multiple ways:

P_{n} = P_{i} + nP_{j}# |

Where i and j are related thus:

(to be continued)

Take any Integer and find the largest p# that is smaller than the Integer. Take the largest multiple of p# away from the Integer that leaves a positive Integer. Is the remainder prime or composite? If composite the likelihood is that the Integer is not prime (but this is not guaranteed). However do the same with the next smaller p#, & follow the same procedure – is the remainder prime or composite. Continue using smaller p#, if the series of remainders are prime seem to be chances of a prime. If the remainders are composite it’s not possible to suggest that the prime factors are, just that it is less likely to be prime