PCR at e=1, c=30: 2^30 = 1,073,741,824 ≈ 10^9-fold amplification

Sympy-exact witness of the PCR amplification identity at canonical anchor values. Setup: N(c; N_0, e) = N_0·(1+e)^c; specialise to e = 1 (ideal 100% efficiency): N(c) = N_0·2^c. At c = 30 cycles, N(30)/N_0 = 2^30 = 1,073,741,824 exactly…