Not really.
On my Mac, using a simple-minded Python program (an interpreted language), it takes around a second to count the primes up to 2**20:
$ time factor count-primes $((2**20)) Limit Count Density 1048576 82025 7.82% real 0m0.986s user 0m0.921s sys 0m0.036s $
Here are the last ten of them:
time factor show-primes $((2**20)) 10 [1048391, 1048423, 1048433, 1048447, 1048507, 1048517, 1048549, 1048559, 1048571, 1048573] real 0m0.755s user 0m0.694s sys 0m0.040s $
Moving up to 2**24, things do slow down:
$ time factor count-primes $((2**24)) Limit Count Density 16777216 1077871 6.42% real 0m15.389s user 0m14.747s sys 0m0.244s $
Am I sort of right about Bitcoin being tied to prime numbers?