--- On Fri, 4/17/09, David Broadhurst <

d.broadhurst@...> wrote:

> Submitted to OEIS:

>

> Numbers n such that 2^x + 3^y is never prime when max(x,y) = n

>

> 1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578,

> 7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749

>

> Mark Underwood found that for each non-negative integer n < 1421

> there is at least one prime of the form 2^m + 3^n or 2^n + 3^m

> with m not exceeding n.

>

> This sequence consists of numbers for which there is no

> such prime.

>

> David Broadhurst estimated that a fraction in excess of 1/800

> of the natural numbers belongs to this sequence and found

> 17 instances with n < 10^4.

>

> For each of the remaining 9983 non-negative integers n < 10^4,

> a prime or probable prime of the form 2^x + 3^y was found with

> max(x,y) = n.

>

> Each probable prime was subjected to a combination of

> strong Fermat and strong Lucas tests.

>

> http://physics.open.ac.uk/~dbroadhu/cert/marktest.txt

This form invites possibly the most bizarre, and remarkably efficient, sieve algorithm I've yet had the misfortune of considering. Good job I'm not coding currently... I'm going to be a tortured soul for at least 2 days until I forget about it.

Phil