Bismillah ArRahman ArRaheem
As Salaam Wa-Alaykum
Semen needs to have all the following three signs before considered to be of the najis form (everything else is considered clean/pure, except urine).
1. Sexual desire
2. Ejaculation of white/milky fluid with force after orgasim (so if it drips out it is not considered semen)
3. The body slackens afterwards. (The body may be slackened already if you are ill, and the ejaculation may not be forceful, so only the first point would be relevant if sick).
See https://www.sistani.org/english/book/49/2397/ for further detail.
In the question specifically asked, the prayers are acceptable with that form of discharge which is without desire and force and body slackened afterwards.