>Yves' table for n=2 does go much further than any of the above.

Just because it's the smallest sequence of primes (defined by a simple

>

>What was the original reason for the need for such primes?

formula) which contains the Fermat and the Mersenne primes. The most simple

generalization (if it exists) of Lucas's tests (a Lucas sequence exists for

the Fermat numbers too) should be able to prove quickly the primality of

these primes.

Yves