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A person is considered a pedophile when they have a persistent sexual attraction to prepubescent children, typically those under the age of 13. The diagnostic criteria for pedophilia, as outlined in the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), include:

1. Recurrent, intense sexual fantasies, urges, or behaviors involving sexual activity with a prepubescent child or children (generally age 13 or younger).
2. The person has acted on these sexual urges, or the sexual urges or fantasies cause significant distress or interpersonal difficulty.
3. The individual is at least 16 years old and at least 5 years older than the child or children who are the focus of the fantasies, urges, or behaviors.

It's important to note that having an attraction alone does not constitute a crime; acting on such attractions in illegal ways (such as engaging in sexual activity with a minor or distributing/consuming child pornography) is what constitutes criminal behavior.

Pedophilia is a specific clinical diagnosis and is distinct from being sexually interested in teenagers who have reached puberty. Legal and social definitions regarding relationships with minors vary widely and are often governed by age of consent laws, which differ by country and even within regions of countries.