Prime Factory problem statement is as follows
Your task is simple:
Find the first two primes above 1 million, whose separate digit sums are also prime.
As example take 23, which is a prime whose digit sum, 5, is also prime.
The solution is the concatenation of the two numbers,
Example: If the first number is 1,234,567
and the second is 8,765,432,
your solution is 12345678765432
Instead of readily jumping into writing into a program to crunch digits, I used WolframAlpha to solve this challenge. Even for free subscribers, WolframAlpha allots a computation time, which, in most of the cases, enough to solve challenges that appear in such websites and other CTF competitions. Apart from mathematical notations, WolframAlpha can understand natural languages to a large extent. Something like “primes > 1 million” in the WolframAlpha expression box or alternatively pasting this query in browser’s address bar, either will do. Quick mental calculations shows that 1,000,033 and 1,000,037 are the first two numbers having a prime sum of digits. Hence, the solution is