You can do it in many ways, two ways are

I.
A) take first thousand numbers that is 0 to 999
First digit can only be 0
second digit can be any of 10 digits 0-9
third and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*10*4*4=160
B) take next 600 numbers that is 1000 to 1599
First digit can only be 1
second digit can be any of 6 digits 0-5
third and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*6*4*4=96
C) take next 70 numbers that is 1600 to 1670
First digit can only be 1
second digit can be only 6
third digit can be only 2, 3 or 5
and fourth digit can be any of the 4 prime digit - 2,3,5,7
so total 1*1*3*4=12
TOTAL = 160+96+12=268

II.
let us see how many such digits are there in 100s as these numbers will get repeated in each 100..
so both digits can be any of 4 prime numbers - 2,3,5,7 thus 4*4=16
now there are 17 hundreds till 1700, so \(17*16=272\)
but we are also counting 1672, 1673, 1675 and 1677 so subtract 4, thus 272-4=268

A