The longest sum of consecutive primes that add to a prime less than 1,000,000 
In Project Euler problem $50,$ the goal is to find the longest sum of consecutive primes that add to a prime less than $1,000,000. $

I have an efficient algorithm to generate a set of primes between $0$ and $N.$
My first algorithm to try this was to brute force it, but that was impossible.
I tried creating a sliding window, but it took much too long to even begin to cover the problem space.
I got to some primes that were summed by $100$+ consecutive primes, but had only run about $5$-$10$% of the problem space.
I'm self-taught, with very little post-secondary education.

Where can I read about or find about an algorithm for efficiently calculating these consecutive primes?
I'm not looking for an answer, but indeed, more for pointers as to what I should be looking for and learning about in order to solve this myself.


Small speed up hint: the prime is clearly going to be odd, so you can rule out about half of the potential sums that way.
If you're looking for the largest such sum, checking things like $2+3,5+7+11,\cdots$ is a waste of time. Structure it differently so that you spend all your time dealing with larger sums. You don't need most of the problem space.
Hopefully this isn't too much of an answer for you.
