A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of all 2 consecutive digits of the number is prime, is
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The prime digits are (2, 3, 5, 7). If we fix 2 at first place, then other (2n – 1) places are filled by all four digits,
so total number of cases = 4 2n–1
Now, sum of 2 consecutive digits is prime when consecutive digits are (2, 3) or (2, 5) then 2 will be fixed at all alternative places
So favourable cases = 2 n . Therefore probability = 
= 2 n . 2 –4n+2 = 2 2 . 2 –3n = 
.
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