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#Japt, 15 14 bytes 1-indexed

õ@[XXÉ]¬nÃfj l 

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##Explanation Implicit input of integer U.
420

õ 

Create an array of integers from 1 to U, inclusive.
[1,2,3,...,420]

@ Ã 

Pass each through a function, where X is the current element

[XXÉ] 

Create an array containing X and X-1.
[[1,0],[2,1],[3,2],...,[420,419]]

¬n 

Join (¬) to a string and convert to an integer.
[10,21,32,...,420419]

fj 

Filter (f) primes.
[43,109,2221,...,420419]

l 

Get the length of the resulting array and implicitly output the result.
51