Is it obligatory to repeat the prayers after discovering traces of semen on the male organ that were not noticed before the prayer, while not recalling a wet dream?

The general rule is that an event should be attributed to the earliest possible time it could have occurred. If a person sees semen but does not recall a wet dream, and does not know when it occurred, they must perform ghusl (ritual bath) and repeat the prayers from the last sleep they had. This applies whether the semen is wet or dry. If it is dry and only a short time has passed since the prayer, it is possible that it occurred before the prayer.

If they are certain it is semen, then ghusl is obligatory, and they must repeat the prayers they performed after seeing it without having taken ghusl.

Ibn Qudamah said: "If one sees semen on their garment... they should repeat the prayers from the latest sleep they had, unless there is an indication that it was before that, in which case they should repeat from the earliest sleep from which it is possible it occurred."