We present simulations of the stretching of a strongly charged, flexible polyelectrolyte chain for long chain lengths particularly focusing on the intermediate force regime, where the Pincus scaling regime occurs. We performed Monte Carlo simulations using the screened Coulomb potential for 200 mM added salt. The number of monomers ranges from 200 to 25000, which includes the experimental value of 5000 for measurements on ssDNA. The simulation force-extension data matches the experimental data over the whole range of forces. For these long chains, the equilibrium structure factor S(k) shows that the chain has two structural regimes. At long length scales, where the electrostatics is fully screened, the chain is a self-avoiding random walk with Flory exponent of 3/5. At short length scales the structure exhibits polyelectrolyte character and is stretched relative to a neutral chain. Under an applied force, S(k) similar to k at low k and the range of the linear scaling expands monotonically to lower k as the force increases. The logarithmic scaling regime at high forces occurs independent of chain length N and agrees with our previous all ion simulations. For N = 5000, the end-to-end extension scales as a function of the applied force as R-z similar to f(gamma), where gamma = 0.60. This value is smaller than the Pincus value of 0.66, but is in agreement with both experiment and neutral polymer simulations that showed larger N is required to reach the Pincus value. We find gamma = 0.67 in agreement with the Pincus value for N = 25000.