Check numbers between 400 and 430

List potential candidates: 401, 403, 407, 409, 411, 413, 417, 419, 421, 427, 429.

$401, 403, 407, 409, 411, 413, 417, 419, 421, 427, 429$

Filter the list for primality

Exclude composite numbers: 403 ($13 \times 31$), 407 ($11 \times 37$), 411 ($3 \times 137$), 413 ($7 \times 59$), 417 ($3 \times 139$), 427 ($7 \times 61$), 429 ($3 \times 143$).

$403, 407, 411, 413, 417, 427, 429 \text{ are composite.}$

Identify remaining prime numbers

The numbers remaining are 401, 409, 419, 421. Counting these gives a total of 4.

$401, 409, 419, 421 \implies \text{Total} = 4$