Theorem A': rows at T_RH = 3,000,175,332,800 row b=43.749: delta <= [0.0000000227292060495095210119151143902100483413535128208290160774306094244065916862967532988841833918693793, 0.0000000227292060495095210119151143902100483413535128208290160774306094244065916862967532988841833918693793] (c=28, T=3e+09, alpha=0.01) row b=50: delta <= [0.000000001305053932128165403897253415577111406201512075998303205424226624430924788193077468299381486613737392, 0.000000001305053932128165403897253415577111406201512075998303205424226624430924788193077468299381486613737392] (c=32, T=1e+11, alpha=0.01) row b=60: delta <= [0.00000000001362031692918922008491316195097917895682854037864237751724474217546853615754862316869552031600230152, 0.00000000001362031692918922008491316195097917895682854037864237751724474217546853615754862316869552031600230152] (c=35, T=3e+12, alpha=0.01) row b=100: delta <= [0.000000000002176576512356475890767206526141348060634746608909498267094241624135036581596687250574598783943988348, 0.000000000002176576512356475890767206526141348060634746608909498267094241624135036581596687250574598783943988348] (c=35.0, T=3e+12, alpha=0.003) row b=300: delta <= [0.000000000001743948098614949609836214751590422837951859593601432731842020581276296132890580030519656139347102711, 0.000000000001743948098614949609836214751590422837951859593601432731842020581276296132890580030519656139347102711] (c=35.0, T=3e+12, alpha=0.003) row b=600: delta <= [0.000000000001662154207877825425835431186664819389203320236215690795313190669010958950205647874630802740588253385, 0.000000000001662154207877825425835431186664819389203320236215690795313190669010958950205647874630802740588253385] (c=35.0, T=3e+12, alpha=0.003) row b=700: delta <= [0.000000000001651115874381233100328837490063564049457216762977554992343046183724058819736147091431691221266135821, 0.000000000001651115874381233100328837490063564049457216762977554992343046183724058819736147091431691221266135821] (c=35.0, T=3e+12, alpha=0.003) row b=1000: delta <= [0.000000000001631626907705593618482663790098843515857819702448160442858536616462222960544972246355476589652622246, 0.000000000001631626907705593618482663790098843515857819702448160442858536616462222960544972246355476589652622246] (c=35.0, T=3e+12, alpha=0.003) row b=3000: delta <= [0.000000000001602015170495932623780535717968552036428428921272745292623404209269005413168004111233162216440947784, 0.000000000001602015170495932623780535717968552036428428921272745292623404209269005413168004111233162216440947784] (c=35.0, T=3e+12, alpha=0.001) built 314 rows in 139 s [A'] coarse: verified contiguously for L in [43.749, 672.749]; first failure (672.749, 672.999) [A'] fine: verified contiguously for L in [43.749, 672.8489999999977]; first failure (672.8489999999977, 672.8509999999976) [gap] L best eps (T_RH) needed eps shortfall 674 1.654e-12 1.649e-12 1x 700 1.652e-12 1.416e-12 1.17x 800 1.643e-12 8.28e-13 1.98x 1000 1.633e-12 3.38e-13 4.83x 1250 1.623e-12 1.381e-13 11.8x 1500 1.617e-12 6.646e-14 24.3x 1750 1.613e-12 3.583e-14 45x 2000 1.61e-12 2.098e-14 76.7x 2250 7.098e-13 1.309e-14 54.2x 2500 1.097e-13 8.581e-15 12.8x 2750 3.173e-14 5.858e-15 5.42x 3000 4.968e-15 4.134e-15 1.2x 3100 4.968e-15 3.626e-15 1.37x 3150 3.549e-15 3.401e-15 1.04x Theorem D: RH to height T* => (R) on [e^L_A, e^3035.502] T = 1e+17: closes = True T = 5.4774e+14: closes = False (first failure at L in (2438.3489999999974, 2438.8489999999974)) T = 7.4009e+15: closes = True T = 2.0134e+15: closes = True T = 1.0502e+15: closes = False (first failure at L in (2864.3489999999974, 2864.8489999999974)) T = 1.4541e+15: closes = True T = 1.2357e+15: closes = False (first failure at L in (2981.8489999999974, 2982.3489999999974)) T = 1.3405e+15: closes = True T = 1.287e+15: closes = False (first failure at L in (3011.8489999999974, 3012.3489999999974)) T = 1.3135e+15: closes = False (first failure at L in (3027.3489999999974, 3027.8489999999974)) T = 1.3269e+15: closes = False (first failure at L in (3034.8489999999974, 3035.3489999999974)) T = 1.3337e+15: closes = True T = 1.3303e+15: closes = True T = 1.3286e+15: closes = True T = 1.3277e+15: closes = True T = 1.3273e+15: closes = False (first failure at L in (3034.8489999999974, 3035.3489999999974)) T = 1.3275e+15: closes = False (first failure at L in (3035.3489999999974, 3035.502)) [D] RH verified up to height 1.3277e+15 suffices for (R) on [e^671.85, e^3035.502]; the method does not reach it at 1.3275e+15 total 680 s