In my laptop for 200 digit numbers
sage: time p=next_prime(10^200)
CPU times: user 1.04 s, sys: 591 µs, total: 1.04 s
Wall time: 1.04 s
sage: time p=next_probable_prime(10^200)
CPU times: user 20.7 ms, sys: 0 ns, total: 20.7 ms
Wall time: 21.8 ms
What return exacty next_probable_prime? When is desired to use it?