f(2000) = 8.01244e-11 f(2488) = 1.5623858e-12 Lemma 2.3 parameters (c=33.6, T=c/eps=3.000000e+12, alpha=0): no log3c 1.569362e-12; with log3c 1.654295e-12 (+5.41%) alpha = 0, T = H: optimum no log3c 1.569272e-12 (c=33.60); optimum with log3c 1.605042e-12 (c=35.16) alpha free, with log3c: 1.604805e-12 (c=35.156, alpha=0.0029) printed 1.570e-12 eps=1.57000e-12: f(L) >= eps exactly for L <= 2487.367 (gap below 2488: 0.6326) with log3c, c=33.6, alpha=0 eps=1.65430e-12: f(L) >= eps exactly for L <= 2480.567 (gap below 2488: 7.433) re-opt, alpha=0 eps=1.60504e-12: f(L) >= eps exactly for L <= 2484.496 (gap below 2488: 3.504) re-opt, alpha free eps=1.60480e-12: f(L) >= eps exactly for L <= 2484.515 (gap below 2488: 3.485) 1.570e-12 x 1.026 eps=1.61082e-12: f(L) >= eps exactly for L <= 2484.029 (gap below 2488: 3.971) 1.570e-12 x 1.08 eps=1.69560e-12: f(L) >= eps exactly for L <= 2477.363 (gap below 2488: 10.64) A needed at L=2488 for printed: 9.43576 A needed at L=2488 for re-opt alpha free: 9.64494