How many two-digit prime numbers have digits adding up to 10?

The two-digit numbers with digit sum 10 are 19, 28, 37, 46, 55, 64, 73, 82 and 91. Every even one and 55 are out at once, leaving 19, 37, 73 and 91. Of these 19, 37 and 73 are prime, but $91=7\times 13$ is not — it is the standard trap that makes people answer 4. So the count is 3.