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Prime Generating Integers

 Published on Saturday, 5th November 2011, 04:00 pm and solved by 9927
Difficulty: Level 5 [15%]

Problem 357

Consider the divisors of $30$: $1,2,3,5,6,10,15,30$.
It can be seen that for every divisor $d$ of $30$, $d + 30 / d$ is prime.

Find the sum of all positive integers $n$ not exceeding $100\,000\,000$
such that for every divisor $d$ of $n$, $d + n / d$ is prime.



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