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Took a few days since I did this over a few evenings since I'm busy between 9am-5pm. :)
The above loop (loop_prime) is not the same as the loop in prime_sum. The above loop use divider indiscriminantly. In prime_sum all the dividers are only prime numbers making the code a bit faster. The efficiency can be further increased by increasing by 2 rather than 1 to skip the even numbers as well which I haven't implemented here yet. All prime numbers are odd apart from 2.

You are right about the sum! I should have tracked it.