Prime numbers are integers greater than 1 that have exactly two factors: 1 and themselves. After 7, the next integer is 8 (not prime, divisible by 2), then 9 (not prime, divisible by 3), then 10 (not prime, divisible by 2 and 5). The number 11 is prime because its only factors are 1 and 11. While 13 is also prime, it is not the next prime after 7.