MathNet 2025 — Part 01 (100 complete bilingual questions) Question 86

Find the prime numbers $a, b, c, d$, with $a \le b$ and $c \le d$, satisfying
(1) $a + b = c + d + 1$;
(2) $a^2 + b^2 + c^2 + d^2 = 3543$.