Prime Numbers which Divide Sum of All Lesser Primes

Theorem
The following sequence of positive integers have the property that each is a divisor of the sum of all primes smaller than them:
 * $2, 5, 71, 369 \, 119, 415 \, 074 \, 643$

As of time of writing (May 2017), no others are known.

Proof
Verified by calculation.