Prime mystery: Solution
The numbers 31, 41, and 59 are the 11th, 13th, and 17th primes where 11, 13 and 17 form three consecutive primes. So the number we get by putting them together, 314159, fulfills the first part of our requirement for the number N.
Now split 314159 into the two numbers 314 and 159. The prime factors of 314 are 2 and 157, which add up to 159. So 314159 also fulfills the second requirement — hence N=314159 is the number we are looking for. It also represents the first six digits of π