log(100000) is 5, so approximately 1 in 5 numbers below 100k is prime. Obviously those in the range 10000-99999 are less dense, but primes are still surprisingly common.
That being said, the pool you're really working from is the numbers with last digit 1, 3, 7, or 9. One out of every 4.6 such numbers under 10^5 is prime. So just guessing until you find a prime is practical.
> On calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log".