Unfortunately, you are _technically_ incorrect. The fact that you can always find an N such that N-1 and N+1 are primes has been conjectured, but it has not been proven. Of course, it's a good as true but you can never be sure. Still a good starting place though.

The algorithm that tye is probably referring to is one which states that you can find an arbitrarily long sequence of sequential composite numbers if you look high enough.

Here it is:
Let D be the length of the composite run.
Let us examine the sequence:

(D+1)!+2,(D+1)!+2,(D+1)!+3,...,(D+1)!+D+1

Then clearly the first term is divisible by 2 (since the factorial is defined as (1*2*...n)), and by the same logic the second term is divisible by 3, and the 3rd by four. Obviously (from the definition of a factorial), all the terms have a factor greater than 2, and this sequence of D numbers is thus composite. QED.

In reply to jweed: Algorithms and such by jweed
in thread Finding the next larger prime. by BrowserUk

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