Distribution of primes (intro)
General · Mathematics
Study notes
Q: Estimate π(1000) using the prime number theorem and compare with truth. Estimate: 1000/ln(1000) = 1000/6.908 = 144.8. Actual: π(1000) = 168. Error ~14%: PNT is asymptotic - improves as x grows! π(10⁶) = 78,498 vs 10⁶/ln(10⁶) = 72,382 (8% off).