5 and 31 7 and 29 13 and 23 17 and 19
The pairs of prime numbers that add up to 36 are 5 and 31, 7 and 29, 13 and 23, and 17 and 19. The possible combinations include one even prime (2), but it cannot add to 36 with another prime. Thus, we focused on pairs of odd primes.
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