Neither letter is silent. Both make the same sound /s/ And when two identical sounds are put together in the same word English, they are almost always said as if they were one sound. So we say [s] instead of [ss].
The fact that the C was added later is irrelevant, as it was likely added because it would not change the pronunciation of the word.
Silent letters in English were usually at one time pronounced (whether in English or the originating language). The P in pneumonia is silent because we don't say /pn/ at the beginning of words. The W in write is silent because we can't say /wr/.
Analyzing a letter as being silent is more of a last resort thing, what you do when no other rule of English orthography will work.