Find large primes with the help of a binary pattern.

Binary numbers: 101, 1101, 11101,111101, 1111111101
,11111111111111111111111111101 all share two things. They
all end in 101 and they are also all prime.

Note that this doesn't always hold. 1111101 is not a prime,
but for primes <=509
this holds 85% of the time. That has to
be useful as a heuristic.

//for primes <=509 this holds 85% of the time. That
has to be useful as a heuristic.//

Are you saying that 85% of primes =<509 are of the
form [1]n01?

This does not mean that 85% of numbers of the form
[1]n01 are prime.

The numbers you describe are of the form 2^n-3.

For the first 10 such numbers (starting with n=3), 6
are prime. For the next 10, only 3 are prime. For
the next 10, only 2 are prime. For the next _30_,
none is prime.

Overall, of the first 60 such numbers (the largest
being about 4,600,000,000,000,000,000), only 11 are
prime, the highest such prime being only
536,870,909.

Nice idea, and neat observation, but it's not likely to
be an efficient way of finding large primes, sadly. It
might be more efficient than just testing all odd
numbers, but it's likely to be much less efficient than
testing, say, Mersenne numbers.