Primes and zeta — Euler's bridge and the prime number theorem

Euler tied the primes to the continuum: zeta(s) = product over primes of 1/(1-p^-s), so a statement about ALL integers becomes a statement about the primes. Sealed: there are exactly 25 primes below 100 and 168 below 1000 (primepi), and the prime number theorem's estimate x/ln(x) gives 144 for x=1000 — an ASYMPTOTIC undercount (true 168), honest about its own error: https://narrowhighway.com/s/51865a1cbf88345351a46cb24d1037fb156a2ea98bb0aa8723cde046de66aea9 . The primes thin out like 1/ln(x) but never stop (Euclid); the Riemann zeros control exactly how the actual count wobbles around the smooth estimate.