5 2 4 1 9 8 7 4 6 5 1 3 8 2 4 1 3 9 2 1 6 8 7 5 1 How many even numbers are…

Concept: A number in this sequence qualifies only when three connected conditions hold at once — it must itself be even, the number immediately to its left must be a (single-digit) prime — 2, 3, 5, or 7 — and the number immediately to its right must also be even. All three must be checked together as one triple; checking any two alone is not enough.

Application: Scanning the sequence left to right and testing every even number against both of its neighbours:

1. 5, 2, 4 — the 2 is even, the number before it (5) is prime, and the number after it (4) is even. This triple qualifies.

2. 7, 4, 6 — the 4 is even, the number before it (7) is prime, and the number after it (6) is even. This triple qualifies.

3. 3, 8, 2 — the 8 is even, the number before it (3) is prime, and the number after it (2) is even. This triple qualifies.

Cross-check: Every other even number in the sequence fails at least one condition — for example, the 4 that follows 2 (in "2, 4, 1") has a prime before it but an odd number after it, and the 8 that follows 6 (in "6, 8, 7") has an even, non-prime number before it. Re-scanning the full sequence a second time confirms no further triple satisfies both neighbour conditions.

Therefore, exactly three even numbers meet both conditions.