Tight/ideal/ropelength-minimized prime knot types


Tight +3.1 p3.1.tight.2400.srgn p3.1.tight.2400.srgn p3.1.tight.2400.srgn

Tight -3.1 m3.1.tight.2400.srgn m3.1.tight.2400.srgn m3.1.tight.2400.srgn

Tight 4.1 a4.1.tight.400.srgn a4.1.tight.400.srgn a4.1.tight.400.srgn

Tight +5.1 p5.1.tight.392.srgn p5.1.tight.392.srgn p5.1.tight.392.srgn

Tight -5.1 m5.1.tight.392.srgn m5.1.tight.392.srgn m5.1.tight.392.srgn

Tight +5.2 p5.2.tight.400.srgn p5.2.tight.400.srgn p5.2.tight.400.srgn

Tight -5.2 m5.2.tight.400.srgn m5.2.tight.400.srgn m5.2.tight.400.srgn

Tight +6.1 p6.1.tight.480.srgn p6.1.tight.480.srgn p6.1.tight.480.srgn

Tight -6.1 m6.1.tight.480.srgn m6.1.tight.480.srgn m6.1.tight.480.srgn

Tight +6.2 p6.2.tight.464.srgn p6.2.tight.464.srgn p6.2.tight.464.srgn

Tight -6.2 m6.2.tight.464.srgn m6.2.tight.464.srgn m6.2.tight.464.srgn

Tight 6.3 a6.3.tight.463.srgn a6.3.tight.463.srgn a6.3.tight.463.srgn

Tight +7.1 p7.1.tight.512.srgn p7.1.tight.512.srgn p7.1.tight.512.srgn

Tight -7.1 m7.1.tight.512.srgn m7.1.tight.512.srgn m7.1.tight.512.srgn

Tight +7.2 p7.2.tight.528.srgn p7.2.tight.528.srgn p7.2.tight.528.srgn

Tight -7.2 m7.2.tight.528.srgn m7.2.tight.528.srgn m7.2.tight.528.srgn

Tight +7.3 p7.3.tight.528.srgn p7.3.tight.528.srgn p7.3.tight.528.srgn

Tight -7.3 m7.3.tight.528.srgn m7.3.tight.528.srgn m7.3.tight.528.srgn

Tight +7.4 p7.4.tight.515.srgn p7.4.tight.515.srgn p7.4.tight.515.srgn

Tight -7.4 m7.4.tight.515.srgn m7.4.tight.515.srgn m7.4.tight.515.srgn

Tight +7.5 p7.5.tight.523.srgn p7.5.tight.523.srgn p7.5.tight.523.srgn

Tight -7.5 m7.5.tight.523.srgn m7.5.tight.523.srgn m7.5.tight.523.srgn

Tight +7.6 p7.6.tight.536.srgn p7.6.tight.536.srgn p7.6.tight.536.srgn

Tight -7.6 m7.6.tight.536.srgn m7.6.tight.536.srgn m7.6.tight.536.srgn

Tight +7.7 p7.7.tight.528.srgn p7.7.tight.528.srgn p7.7.tight.528.srgn

Tight -7.7 m7.7.tight.528.srgn m7.7.tight.528.srgn m7.7.tight.528.srgn

Tight +8.1 p8.1.tight.592.srgn p8.1.tight.592.srgn p8.1.tight.592.srgn

Tight -8.1 m8.1.tight.592.srgn m8.1.tight.592.srgn m8.1.tight.592.srgn

Tight +8.2 p8.2.tight.572.srgn p8.2.tight.572.srgn p8.2.tight.572.srgn

Tight -8.2 m8.2.tight.572.srgn m8.2.tight.572.srgn m8.2.tight.572.srgn

Tight 8.3 a8.3.tight.570.srgn a8.3.tight.570.srgn a8.3.tight.570.srgn

Tight +8.4 p8.4.tight.600.srgn p8.4.tight.600.srgn p8.4.tight.600.srgn

Tight -8.4 m8.4.tight.600.srgn m8.4.tight.600.srgn m8.4.tight.600.srgn

Tight +8.5 p8.5.tight.592.srgn p8.5.tight.592.srgn p8.5.tight.592.srgn

Tight -8.5 m8.5.tight.592.srgn m8.5.tight.592.srgn m8.5.tight.592.srgn

Tight +8.6 p8.6.tight.581.srgn p8.6.tight.581.srgn p8.6.tight.581.srgn

Tight -8.6 m8.6.tight.581.srgn m8.6.tight.581.srgn m8.6.tight.581.srgn

Tight +8.7 p8.7.tight.584.srgn p8.7.tight.584.srgn p8.7.tight.584.srgn

Tight -8.7 m8.7.tight.584.srgn m8.7.tight.584.srgn m8.7.tight.584.srgn

Tight +8.8 p8.8.tight.584.srgn p8.8.tight.584.srgn p8.8.tight.584.srgn

Tight -8.8 m8.8.tight.584.srgn m8.8.tight.584.srgn m8.8.tight.584.srgn

Tight 8.9 a8.9.tight.580.srgn a8.9.tight.580.srgn a8.9.tight.580.srgn

Tight +8.10 p8.10.tight.585.srgn p8.10.tight.585.srgn p8.10.tight.585.srgn

Tight -8.10 m8.10.tight.585.srgn m8.10.tight.585.srgn m8.10.tight.585.srgn

Tight +8.11 p8.11.tight.585.srgn p8.11.tight.585.srgn p8.11.tight.585.srgn

Tight -8.11 m8.11.tight.585.srgn m8.11.tight.585.srgn m8.11.tight.585.srgn

Tight 8.12 a8.12.tight.608.srgn a8.12.tight.608.srgn a8.12.tight.608.srgn

Tight +8.13 p8.13.tight.583.srgn p8.13.tight.583.srgn p8.13.tight.583.srgn

Tight -8.13 m8.13.tight.583.srgn m8.13.tight.583.srgn m8.13.tight.583.srgn

Tight +8.14 p8.14.tight.600.srgn p8.14.tight.600.srgn p8.14.tight.600.srgn

Tight -8.14 m8.14.tight.600.srgn m8.14.tight.600.srgn m8.14.tight.600.srgn

Tight +8.15 p8.15.tight.593.srgn p8.15.tight.593.srgn p8.15.tight.593.srgn

Tight -8.15 m8.15.tight.593.srgn m8.15.tight.593.srgn m8.15.tight.593.srgn

Tight +8.16 p8.16.tight.590.srgn p8.16.tight.590.srgn p8.16.tight.590.srgn

Tight -8.16 m8.16.tight.590.srgn m8.16.tight.590.srgn m8.16.tight.590.srgn

Tight 8.17 a8.17.tight.608.srgn a8.17.tight.608.srgn a8.17.tight.608.srgn

Tight 8.18 a8.18.tight.1199.srgn a8.18.tight.1199.srgn a8.18.tight.1199.srgn

Tight +8.19 p8.19.tight.489.srgn p8.19.tight.489.srgn p8.19.tight.489.srgn

Tight -8.19 m8.19.tight.489.srgn m8.19.tight.489.srgn m8.19.tight.489.srgn

Tight +8.20 p8.20.tight.528.srgn p8.20.tight.528.srgn p8.20.tight.528.srgn

Tight -8.20 m8.20.tight.528.srgn m8.20.tight.528.srgn m8.20.tight.528.srgn

Tight +8.21 p8.21.tight.525.srgn p8.21.tight.525.srgn p8.21.tight.525.srgn

Tight -8.21 m8.21.tight.525.srgn m8.21.tight.525.srgn m8.21.tight.525.srgn

Tight +9.1 p9.1.tight.624.srgn p9.1.tight.624.srgn p9.1.tight.624.srgn

Tight -9.1 m9.1.tight.624.srgn m9.1.tight.624.srgn m9.1.tight.624.srgn

Tight +9.2 p9.2.tight.640.srgn p9.2.tight.640.srgn p9.2.tight.640.srgn

Tight -9.2 m9.2.tight.640.srgn m9.2.tight.640.srgn m9.2.tight.640.srgn

Tight +9.3 p9.3.tight.640.srgn p9.3.tight.640.srgn p9.3.tight.640.srgn

Tight -9.3 m9.3.tight.640.srgn m9.3.tight.640.srgn m9.3.tight.640.srgn

Tight +9.4 p9.4.tight.648.srgn p9.4.tight.648.srgn p9.4.tight.648.srgn

Tight -9.4 m9.4.tight.648.srgn m9.4.tight.648.srgn m9.4.tight.648.srgn

Tight +9.5 p9.5.tight.648.srgn p9.5.tight.648.srgn p9.5.tight.648.srgn

Tight -9.5 m9.5.tight.648.srgn m9.5.tight.648.srgn m9.5.tight.648.srgn

Tight +9.6 p9.6.tight.639.srgn p9.6.tight.639.srgn p9.6.tight.639.srgn

Tight -9.6 m9.6.tight.639.srgn m9.6.tight.639.srgn m9.6.tight.639.srgn

Tight +9.7 p9.7.tight.656.srgn p9.7.tight.656.srgn p9.7.tight.656.srgn

Tight -9.7 m9.7.tight.656.srgn m9.7.tight.656.srgn m9.7.tight.656.srgn

Tight +9.8 p9.8.tight.656.srgn p9.8.tight.656.srgn p9.8.tight.656.srgn

Tight -9.8 m9.8.tight.656.srgn m9.8.tight.656.srgn m9.8.tight.656.srgn

Tight +9.9 p9.9.tight.640.srgn p9.9.tight.640.srgn p9.9.tight.640.srgn

Tight -9.9 m9.9.tight.640.srgn m9.9.tight.640.srgn m9.9.tight.640.srgn

Tight +9.10 p9.10.tight.656.srgn p9.10.tight.656.srgn p9.10.tight.656.srgn

Tight -9.10 m9.10.tight.656.srgn m9.10.tight.656.srgn m9.10.tight.656.srgn

Tight +9.11 p9.11.tight.643.srgn p9.11.tight.643.srgn p9.11.tight.643.srgn

Tight -9.11 m9.11.tight.643.srgn m9.11.tight.643.srgn m9.11.tight.643.srgn

Tight +9.12 p9.12.tight.664.srgn p9.12.tight.664.srgn p9.12.tight.664.srgn

Tight -9.12 m9.12.tight.664.srgn m9.12.tight.664.srgn m9.12.tight.664.srgn

Tight +9.13 p9.13.tight.656.srgn p9.13.tight.656.srgn p9.13.tight.656.srgn

Tight -9.13 m9.13.tight.656.srgn m9.13.tight.656.srgn m9.13.tight.656.srgn

Tight +9.14 p9.14.tight.672.srgn p9.14.tight.672.srgn p9.14.tight.672.srgn

Tight -9.14 m9.14.tight.672.srgn m9.14.tight.672.srgn m9.14.tight.672.srgn

Tight +9.15 p9.15.tight.649.srgn p9.15.tight.649.srgn p9.15.tight.649.srgn

Tight -9.15 m9.15.tight.649.srgn m9.15.tight.649.srgn m9.15.tight.649.srgn

Tight +9.16 p9.16.tight.642.srgn p9.16.tight.642.srgn p9.16.tight.642.srgn

Tight -9.16 m9.16.tight.642.srgn m9.16.tight.642.srgn m9.16.tight.642.srgn

Tight +9.17 p9.17.tight.645.srgn p9.17.tight.645.srgn p9.17.tight.645.srgn

Tight -9.17 m9.17.tight.645.srgn m9.17.tight.645.srgn m9.17.tight.645.srgn

Tight +9.18 p9.18.tight.654.srgn p9.18.tight.654.srgn p9.18.tight.654.srgn

Tight -9.18 m9.18.tight.654.srgn m9.18.tight.654.srgn m9.18.tight.654.srgn

Tight +9.19 p9.19.tight.650.srgn p9.19.tight.650.srgn p9.19.tight.650.srgn

Tight -9.19 m9.19.tight.650.srgn m9.19.tight.650.srgn m9.19.tight.650.srgn

Tight +9.20 p9.20.tight.643.srgn p9.20.tight.643.srgn p9.20.tight.643.srgn

Tight -9.20 m9.20.tight.643.srgn m9.20.tight.643.srgn m9.20.tight.643.srgn

Tight +9.21 p9.21.tight.650.srgn p9.21.tight.650.srgn p9.21.tight.650.srgn

Tight -9.21 m9.21.tight.650.srgn m9.21.tight.650.srgn m9.21.tight.650.srgn

Tight +9.22 p9.22.tight.649.srgn p9.22.tight.649.srgn p9.22.tight.649.srgn

Tight -9.22 m9.22.tight.649.srgn m9.22.tight.649.srgn m9.22.tight.649.srgn

Tight +9.23 p9.23.tight.651.srgn p9.23.tight.651.srgn p9.23.tight.651.srgn

Tight -9.23 m9.23.tight.651.srgn m9.23.tight.651.srgn m9.23.tight.651.srgn

Tight +9.24 p9.24.tight.648.srgn p9.24.tight.648.srgn p9.24.tight.648.srgn

Tight -9.24 m9.24.tight.648.srgn m9.24.tight.648.srgn m9.24.tight.648.srgn

Tight +9.25 p9.25.tight.696.srgn p9.25.tight.696.srgn p9.25.tight.696.srgn

Tight -9.25 m9.25.tight.696.srgn m9.25.tight.696.srgn m9.25.tight.696.srgn

Tight +9.26 p9.26.tight.648.srgn p9.26.tight.648.srgn p9.26.tight.648.srgn

Tight -9.26 m9.26.tight.648.srgn m9.26.tight.648.srgn m9.26.tight.648.srgn

Tight +9.27 p9.27.tight.664.srgn p9.27.tight.664.srgn p9.27.tight.664.srgn

Tight -9.27 m9.27.tight.664.srgn m9.27.tight.664.srgn m9.27.tight.664.srgn

Tight +9.28 p9.28.tight.664.srgn p9.28.tight.664.srgn p9.28.tight.664.srgn

Tight -9.28 m9.28.tight.664.srgn m9.28.tight.664.srgn m9.28.tight.664.srgn

Tight +9.29 p9.29.tight.652.srgn p9.29.tight.652.srgn p9.29.tight.652.srgn

Tight -9.29 m9.29.tight.652.srgn m9.29.tight.652.srgn m9.29.tight.652.srgn

Tight +9.30 p9.30.tight.672.srgn p9.30.tight.672.srgn p9.30.tight.672.srgn

Tight -9.30 m9.30.tight.672.srgn m9.30.tight.672.srgn m9.30.tight.672.srgn

Tight +9.31 p9.31.tight.655.srgn p9.31.tight.655.srgn p9.31.tight.655.srgn

Tight -9.31 m9.31.tight.655.srgn m9.31.tight.655.srgn m9.31.tight.655.srgn

Tight +9.32 p9.32.tight.653.srgn p9.32.tight.653.srgn p9.32.tight.653.srgn

Tight -9.32 m9.32.tight.653.srgn m9.32.tight.653.srgn m9.32.tight.653.srgn

Tight +9.33 p9.33.tight.662.srgn p9.33.tight.662.srgn p9.33.tight.662.srgn

Tight -9.33 m9.33.tight.662.srgn m9.33.tight.662.srgn m9.33.tight.662.srgn

Tight +9.34 p9.34.tight.658.srgn p9.34.tight.658.srgn p9.34.tight.658.srgn

Tight -9.34 m9.34.tight.658.srgn m9.34.tight.658.srgn m9.34.tight.658.srgn

Tight +9.35 p9.35.tight.648.srgn p9.35.tight.648.srgn p9.35.tight.648.srgn

Tight -9.35 m9.35.tight.648.srgn m9.35.tight.648.srgn m9.35.tight.648.srgn

Tight +9.36 p9.36.tight.644.srgn p9.36.tight.644.srgn p9.36.tight.644.srgn

Tight -9.36 m9.36.tight.644.srgn m9.36.tight.644.srgn m9.36.tight.644.srgn

Tight +9.37 p9.37.tight.664.srgn p9.37.tight.664.srgn p9.37.tight.664.srgn

Tight -9.37 m9.37.tight.664.srgn m9.37.tight.664.srgn m9.37.tight.664.srgn

Tight +9.38 p9.38.tight.655.srgn p9.38.tight.655.srgn p9.38.tight.655.srgn

Tight -9.38 m9.38.tight.655.srgn m9.38.tight.655.srgn m9.38.tight.655.srgn

Tight +9.39 p9.39.tight.656.srgn p9.39.tight.656.srgn p9.39.tight.656.srgn

Tight -9.39 m9.39.tight.656.srgn m9.39.tight.656.srgn m9.39.tight.656.srgn

Tight +9.40 p9.40.tight.654.srgn p9.40.tight.654.srgn p9.40.tight.654.srgn

Tight -9.40 m9.40.tight.654.srgn m9.40.tight.654.srgn m9.40.tight.654.srgn

Tight +9.41 p9.41.tight.736.srgn p9.41.tight.736.srgn p9.41.tight.736.srgn

Tight -9.41 m9.41.tight.736.srgn m9.41.tight.736.srgn m9.41.tight.736.srgn

Tight +9.42 p9.42.tight.557.srgn p9.42.tight.557.srgn p9.42.tight.557.srgn

Tight -9.42 m9.42.tight.557.srgn m9.42.tight.557.srgn m9.42.tight.557.srgn

Tight +9.43 p9.43.tight.574.srgn p9.43.tight.574.srgn p9.43.tight.574.srgn

Tight -9.43 m9.43.tight.574.srgn m9.43.tight.574.srgn m9.43.tight.574.srgn

Tight +9.44 p9.44.tight.608.srgn p9.44.tight.608.srgn p9.44.tight.608.srgn

Tight -9.44 m9.44.tight.608.srgn m9.44.tight.608.srgn m9.44.tight.608.srgn

Tight +9.45 p9.45.tight.608.srgn p9.45.tight.608.srgn p9.45.tight.608.srgn

Tight -9.45 m9.45.tight.608.srgn m9.45.tight.608.srgn m9.45.tight.608.srgn

Tight +9.46 p9.46.tight.552.srgn p9.46.tight.552.srgn p9.46.tight.552.srgn

Tight -9.46 m9.46.tight.552.srgn m9.46.tight.552.srgn m9.46.tight.552.srgn

Tight +9.47 p9.47.tight.616.srgn p9.47.tight.616.srgn p9.47.tight.616.srgn

Tight -9.47 m9.47.tight.616.srgn m9.47.tight.616.srgn m9.47.tight.616.srgn

Tight +9.48 p9.48.tight.608.srgn p9.48.tight.608.srgn p9.48.tight.608.srgn

Tight -9.48 m9.48.tight.608.srgn m9.48.tight.608.srgn m9.48.tight.608.srgn

Tight +9.49 p9.49.tight.593.srgn p9.49.tight.593.srgn p9.49.tight.593.srgn

Tight -9.49 m9.49.tight.593.srgn m9.49.tight.593.srgn m9.49.tight.593.srgn

Tight +10.1 p10.1.tight.688.srgn p10.1.tight.688.srgn p10.1.tight.688.srgn

Tight -10.1 m10.1.tight.688.srgn m10.1.tight.688.srgn m10.1.tight.688.srgn

Tight +10.2 p10.2.tight.712.srgn p10.2.tight.712.srgn p10.2.tight.712.srgn

Tight -10.2 m10.2.tight.712.srgn m10.2.tight.712.srgn m10.2.tight.712.srgn

Tight +10.3 p10.3.tight.686.srgn p10.3.tight.686.srgn p10.3.tight.686.srgn

Tight -10.3 m10.3.tight.686.srgn m10.3.tight.686.srgn m10.3.tight.686.srgn

Tight +10.4 p10.4.tight.696.srgn p10.4.tight.696.srgn p10.4.tight.696.srgn

Tight -10.4 m10.4.tight.696.srgn m10.4.tight.696.srgn m10.4.tight.696.srgn

Tight +10.5 p10.5.tight.696.srgn p10.5.tight.696.srgn p10.5.tight.696.srgn

Tight -10.5 m10.5.tight.696.srgn m10.5.tight.696.srgn m10.5.tight.696.srgn

Tight +10.6 p10.6.tight.697.srgn p10.6.tight.697.srgn p10.6.tight.697.srgn

Tight -10.6 m10.6.tight.697.srgn m10.6.tight.697.srgn m10.6.tight.697.srgn

Tight +10.7 p10.7.tight.702.srgn p10.7.tight.702.srgn p10.7.tight.702.srgn

Tight -10.7 m10.7.tight.702.srgn m10.7.tight.702.srgn m10.7.tight.702.srgn

Tight +10.8 p10.8.tight.720.srgn p10.8.tight.720.srgn p10.8.tight.720.srgn

Tight -10.8 m10.8.tight.720.srgn m10.8.tight.720.srgn m10.8.tight.720.srgn

Tight +10.9 p10.9.tight.720.srgn p10.9.tight.720.srgn p10.9.tight.720.srgn

Tight -10.9 m10.9.tight.720.srgn m10.9.tight.720.srgn m10.9.tight.720.srgn

Tight +10.10 p10.10.tight.712.srgn p10.10.tight.712.srgn p10.10.tight.712.srgn

Tight -10.10 m10.10.tight.712.srgn m10.10.tight.712.srgn m10.10.tight.712.srgn

Tight +10.11 p10.11.tight.698.srgn p10.11.tight.698.srgn p10.11.tight.698.srgn

Tight -10.11 m10.11.tight.698.srgn m10.11.tight.698.srgn m10.11.tight.698.srgn

Tight +10.12 p10.12.tight.699.srgn p10.12.tight.699.srgn p10.12.tight.699.srgn

Tight -10.12 m10.12.tight.699.srgn m10.12.tight.699.srgn m10.12.tight.699.srgn

Tight +10.13 p10.13.tight.712.srgn p10.13.tight.712.srgn p10.13.tight.712.srgn

Tight -10.13 m10.13.tight.712.srgn m10.13.tight.712.srgn m10.13.tight.712.srgn

Tight +10.14 p10.14.tight.736.srgn p10.14.tight.736.srgn p10.14.tight.736.srgn

Tight -10.14 m10.14.tight.736.srgn m10.14.tight.736.srgn m10.14.tight.736.srgn

Tight +10.15 p10.15.tight.712.srgn p10.15.tight.712.srgn p10.15.tight.712.srgn

Tight -10.15 m10.15.tight.712.srgn m10.15.tight.712.srgn m10.15.tight.712.srgn

Tight +10.16 p10.16.tight.702.srgn p10.16.tight.702.srgn p10.16.tight.702.srgn

Tight -10.16 m10.16.tight.702.srgn m10.16.tight.702.srgn m10.16.tight.702.srgn

Tight 10.17 a10.17.tight.712.srgn a10.17.tight.712.srgn a10.17.tight.712.srgn

Tight +10.18 p10.18.tight.728.srgn p10.18.tight.728.srgn p10.18.tight.728.srgn

Tight -10.18 m10.18.tight.728.srgn m10.18.tight.728.srgn m10.18.tight.728.srgn

Tight +10.19 p10.19.tight.703.srgn p10.19.tight.703.srgn p10.19.tight.703.srgn

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This material is based upon work supported by the National Science Foundation under Grant Nos. 1115722, 1418869, and 1720342 for E. Rawdon, by the University of Pittsburgh, Graz University of Technology, Vanderbilt University, Austrian Science Fund (FWF) Project 5503, and National Science Foundation Grant Nos. 1516400 and 1104102 for W. Kusner, by National Science Centre (Poland) under Grant 2015/19/D/ST8/03199 for P. Szymczak, and by National Science Foundation Grant Nos. 1440140, 1439786, and 1607611 for R. Kusner. G. Dietler, R. Kusner, E. Rawdon, and P. Szymczak were supported by the Newton Institute in 2012.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.