data/problems/134.yml
---
:id: 134
:name: Prime pair connection
:url: https://projecteuler.net/problem=134
:content: |+
Consider the consecutive primes _p_<sub>1</sub> = 19 and _p_<sub>2</sub> = 23. It can be verified that 1219 is the smallest number such that the last digits are formed by _p_<sub>1</sub> whilst also being divisible by _p_<sub>2</sub>.
In fact, with the exception of _p_<sub>1</sub> = 3 and _p_<sub>2</sub> = 5, for every pair of consecutive primes, _p_<sub>2</sub> \> _p_<sub>1</sub>, there exist values of _n_ for which the last digits are formed by _p_<sub>1</sub> and _n_ is divisible by _p_<sub>2</sub>. Let _S_ be the smallest of these values of _n_.
Find ∑ _S_ for every pair of consecutive primes with 5 ≤ _p_<sub>1</sub> ≤ 1000000.