Yes
A prime number is one that has as its factors only itself and 1. So for instance 3 is a prime number and 4 is not:
##1xx3=3## and that’s all we can get for 3 so 3 is prime
##1xx4=4 2xx2=4## – 4 has two sets of factors and so isn’t prime
So are there any factors for 43 other than ##43xx1##?
The quick answer is no and so 43 is prime.
The longer answer is that we can try to multiply numbers to get to 43:
43 is odd and so nothing times 2 will work
##4+3=7## which is not divisible by 3 so nothing times 3 will work
43 doesn’t end in 0 or 5 so nothing times 5 will work
##7xx6=42##. Close but no cigar – nothing times 7 will work
##11xx4=44##. Close again but still no – so nothing times 11 will work
##13xx3=39##. Not so close and still doesn’t work – so nothing times 13 will work
##17xx2=34 17xx3=51##. Not close at all and still doesn’t work – so nothing times 17 will work.
##19xx2=38 19xx3=57##. Nope – nothing times 19 works
##23xx2=46##. Nope.
And there’s no sense in continuing – if 2 times 23 is too big nothing beyond this point will be smaller. And in fact we could have stopped much earlier because we already knew anything times 2 3 4 5… wouldn’t work (I think technically the last attempt that was redundant was seeing that 5 was not a factor – but it was good to show definitively that these bigger numbers wouldn’t work).