1
12 - any number that ends on a multiple of 2 is an even number and hence can't be prime
123 - any number whose sum of digits is divisible by 3 is not a prime
1234 - covered in 12 above
12345 - any number whose last digit is a 5 (or 0) is evenly divisible by and hence can't be a prime
123456 - covered in 12 and 123 above
1234567 - the first possible candidate not immediately eliminatable based on consistuent digits
12345678 - covered in 12
123456789 - covered in 123 above
1234567890 - covered in 12 and 12345 above
Now we start adding the same sequence back
12345678901 - second possible candidate
same rules eliminate all of these up to
12345678901234567

Which means out of each ten digits there are only two candidates for primes - a number ending in 1 or a number ending in 7.

Except that every 3 1-0s they can be eliminated as a multiple of 3
Every 5 1-0s they can be eliminated as a multiple of 5
Every 6 1-0s they can be eliminated as per 3 1-0s above
Every 9 1-0s they can be eliminated as per 3 1-0s above

So while ostensibly there are potentially 20% primes in the 1-0 sequence, 40% of those are eliminated in the up-to 10 such sequences, and so on and so on. In fact as you get larger numbers, the predictive nature of the sum of the digits at any juncture allows eliminating more and more numbers asymptotically reaching zero.

E