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埃拉托斯特尼筛法（质数筛选可视化）

埃拉托斯特尼筛法（质数筛选可视化）
几何画板及绘图内容加载中，请稍等……
2020-06-25 18:15
多边形函数数列滑块动画函数图像
① 本范例通过动态网格与多边形标记，直观演示了埃拉托斯特尼筛法筛选质数的完整过程，即从自然数序列中逐步划去合数，最终留下质数。② 核心数学概念包括质数与合数的定义、整除性、以及经典筛法算法；同时涉及数列生成与条件判断。③ 作图要点：利用GeoGebra的Sequence命令生成自然数序列，If命令进行条件判断（如是否为质数），Polygon命令绘制标记区域；对象包括A0、dy、dx、L1、mode、text1至text26等，用于控制网格尺寸、文本标签和筛选状态。④ 适合中学数学（如数论启蒙）或算法教学，也可用于大学离散数学中质数分布的直观演示，帮助理解筛法效率与质数分布规律。

GeoGebra 命令及参数

  1. Sequence(Segment[(i, 0), (i, 10)], i, 0, 10) → L1
  2. Sequence(Segment[(i, -5), (i, 10)], i, 0, 7) → L5
  3. If(mode ≟ 2, A1 + (0, -1), A1 + (6, 0)) → A7
  4. If(mode ≟ 1, A1 + (7, 0), If[mode ≟ 2, A1 + (1, -1), A1 + (0, -1)]) → A8
  5. If(mode ≟ 1, A1 + (8, 0), If[mode ≟ 2, A1 + (2, -1), A1 + (1, -1)]) → A9
  6. If(mode ≟ 1, A1 + (9, 0), If[mode ≟ 2, A1 + (3, -1), A1 + (2, -1)]) → A10
  7. Sequence(Segment[(0, i), (7, i)], i, -5, 10) → L6
  8. Sequence(Segment[(0, i), (6, i)], i, -7, 10) → L3
  9. Sequence(Segment[(i, -7), (i, 10)], i, 0, 6) → L4
  10. If(mode ≟ 1, A1 + (0, -1), If[mode ≟ 2, A1 + (4, -1), A1 + (3, -1)]) → A11
  11. If(mode ≟ 1, A1 + (1, -1), If[mode ≟ 2, A1 + (5, -1), A1 + (4, -1)]) → A12
  12. If(mode ≟ 1, A1 + (2, -1), If[mode ≟ 2, A1 + (0, -2), A1 + (5, -1)]) → A13
  13. If(mode ≟ 1, A1 + (3, -1), If[mode ≟ 2, A1 + (1, -2), A1 + (6, -1)]) → A14
  14. If(mode ≟ 1, A1 + (4, -1), If[mode ≟ 2, A1 + (2, -2), A1 + (0, -2)]) → A15
  15. If(mode ≟ 1, A1 + (5, -1), If[mode ≟ 2, A1 + (3, -2), A1 + (1, -2)]) → A16
  16. If(mode ≟ 1, A1 + (6, -1), If[mode ≟ 2, A1 + (4, -2), A1 + (2, -2)]) → A17
  17. If(mode ≟ 1, A1 + (7, -1), If[mode ≟ 2, A1 + (5, -2), A1 + (3, -2)]) → A18
  18. If(mode ≟ 1, A1 + (8, -1), If[mode ≟ 2, A1 + (0, -3), A1 + (4, -2)]) → A19
  19. If(mode ≟ 1, A1 + (9, -1), If[mode ≟ 2, A1 + (1, -3), A1 + (5, -2)]) → A20
  20. If(mode ≟ 1, A1 + (0, -2), If[mode ≟ 2, A1 + (2, -3), A1 + (6, -2)]) → A21
  21. If(mode ≟ 1, A1 + (1, -2), If[mode ≟ 2, A1 + (3, -3), A1 + (0, -3)]) → A22
  22. If(mode ≟ 1, A1 + (2, -2), If[mode ≟ 2, A1 + (4, -3), A1 + (1, -3)]) → A23
  23. If(mode ≟ 1, A1 + (3, -2), If[mode ≟ 2, A1 + (5, -3), A1 + (2, -3)]) → A24
  24. If(mode ≟ 1, A1 + (4, -2), If[mode ≟ 2, A1 + (0, -4), A1 + (3, -3)]) → A25
  25. If(mode ≟ 1, A1 + (5, -2), If[mode ≟ 2, A1 + (1, -4), A1 + (4, -3)]) → A26
  26. If(mode ≟ 1, A1 + (6, -2), If[mode ≟ 2, A1 + (2, -4), A1 + (5, -3)]) → A27
  27. If(mode ≟ 1, A1 + (7, -2), If[mode ≟ 2, A1 + (3, -4), A1 + (6, -3)]) → A28
  28. If(mode ≟ 1, A1 + (8, -2), If[mode ≟ 2, A1 + (4, -4), A1 + (0, -4)]) → A29
  29. If(mode ≟ 1, A1 + (9, -2), If[mode ≟ 2, A1 + (5, -4), A1 + (1, -4)]) → A30
  30. If(mode ≟ 1, A1 + (0, -3), If[mode ≟ 2, A1 + (0, -5), A1 + (2, -4)]) → A31
  31. If(mode ≟ 1, A1 + (1, -3), If[mode ≟ 2, A1 + (1, -5), A1 + (3, -4)]) → A32
  32. If(mode ≟ 1, A1 + (2, -3), If[mode ≟ 2, A1 + (2, -5), A1 + (4, -4)]) → A33
  33. If(mode ≟ 1, A1 + (3, -3), If[mode ≟ 2, A1 + (3, -5), A1 + (5, -4)]) → A34
  34. If(mode ≟ 1, A1 + (4, -3), If[mode ≟ 2, A1 + (4, -5), A1 + (6, -4)]) → A35
  35. If(mode ≟ 1, A1 + (5, -3), If[mode ≟ 2, A1 + (5, -5), A1 + (0, -5)]) → A36
  36. If(mode ≟ 1, A1 + (6, -3), If[mode ≟ 2, A1 + (0, -6), A1 + (1, -5)]) → A37
  37. If(mode ≟ 1, A1 + (7, -3), If[mode ≟ 2, A1 + (1, -6), A1 + (2, -5)]) → A38
  38. If(mode ≟ 1, A1 + (8, -3), If[mode ≟ 2, A1 + (2, -6), A1 + (3, -5)]) → A39
  39. If(mode ≟ 1, A1 + (9, -3), If[mode ≟ 2, A1 + (3, -6), A1 + (4, -5)]) → A40
  40. If(mode ≟ 1, A1 + (0, -4), If[mode ≟ 2, A1 + (4, -6), A1 + (5, -5)]) → A41
  41. If(mode ≟ 1, A1 + (1, -4), If[mode ≟ 2, A1 + (5, -6), A1 + (6, -5)]) → A42
  42. If(mode ≟ 1, A1 + (2, -4), If[mode ≟ 2, A1 + (0, -7), A1 + (0, -6)]) → A43
  43. If(mode ≟ 1, A1 + (3, -4), If[mode ≟ 2, A1 + (1, -7), A1 + (1, -6)]) → A44
  44. If(mode ≟ 1, A1 + (4, -4), If[mode ≟ 2, A1 + (2, -7), A1 + (2, -6)]) → A45
  45. If(mode ≟ 1, A1 + (5, -4), If[mode ≟ 2, A1 + (3, -7), A1 + (3, -6)]) → A46
  46. If(mode ≟ 1, A1 + (6, -4), If[mode ≟ 2, A1 + (4, -7), A1 + (4, -6)]) → A47
  47. If(mode ≟ 1, A1 + (7, -4), If[mode ≟ 2, A1 + (5, -7), A1 + (5, -6)]) → A48
  48. If(mode ≟ 1, A1 + (8, -4), If[mode ≟ 2, A1 + (0, -8), A1 + (6, -6)]) → A49
  49. If(mode ≟ 1, A1 + (9, -4), If[mode ≟ 2, A1 + (1, -8), A1 + (0, -7)]) → A50
  50. If(mode ≟ 1, A1 + (0, -5), If[mode ≟ 2, A1 + (2, -8), A1 + (1, -7)]) → A51
  51. If(mode ≟ 1, A1 + (1, -5), If[mode ≟ 2, A1 + (3, -8), A1 + (2, -7)]) → A52
  52. If(mode ≟ 1, A1 + (2, -5), If[mode ≟ 2, A1 + (4, -8), A1 + (3, -7)]) → A53
  53. If(mode ≟ 1, A1 + (3, -5), If[mode ≟ 2, A1 + (5, -8), A1 + (4, -7)]) → A54
  54. If(mode ≟ 1, A1 + (4, -5), If[mode ≟ 2, A1 + (0, -9), A1 + (5, -7)]) → A55
  55. If(mode ≟ 1, A1 + (5, -5), If[mode ≟ 2, A1 + (1, -9), A1 + (6, -7)]) → A56
  56. If(mode ≟ 1, A1 + (6, -5), If[mode ≟ 2, A1 + (2, -9), A1 + (0, -8)]) → A57
  57. If(mode ≟ 1, A1 + (7, -5), If[mode ≟ 2, A1 + (3, -9), A1 + (1, -8)]) → A58
  58. If(mode ≟ 1, A1 + (8, -5), If[mode ≟ 2, A1 + (4, -9), A1 + (2, -8)]) → A59
  59. If(mode ≟ 1, A1 + (9, -5), If[mode ≟ 2, A1 + (5, -9), A1 + (3, -8)]) → A60
  60. If(mode ≟ 1, A1 + (0, -6), If[mode ≟ 2, A1 + (0, -10), A1 + (4, -8)]) → A61
  61. If(mode ≟ 1, A1 + (1, -6), If[mode ≟ 2, A1 + (1, -10), A1 + (5, -8)]) → A62
  62. If(mode ≟ 1, A1 + (2, -6), If[mode ≟ 2, A1 + (2, -10), A1 + (6, -8)]) → A63
  63. If(mode ≟ 1, A1 + (3, -6), If[mode ≟ 2, A1 + (3, -10), A1 + (0, -9)]) → A64
  64. If(mode ≟ 1, A1 + (4, -6), If[mode ≟ 2, A1 + (4, -10), A1 + (1, -9)]) → A65
  65. If(mode ≟ 1, A1 + (5, -6), If[mode ≟ 2, A1 + (5, -10), A1 + (2, -9)]) → A66
  66. If(mode ≟ 1, A1 + (6, -6), If[mode ≟ 2, A1 + (0, -11), A1 + (3, -9)]) → A67
  67. If(mode ≟ 1, A1 + (7, -6), If[mode ≟ 2, A1 + (1, -11), A1 + (4, -9)]) → A68
  68. If(mode ≟ 1, A1 + (8, -6), If[mode ≟ 2, A1 + (2, -11), A1 + (5, -9)]) → A69
  69. If(mode ≟ 1, A1 + (9, -6), If[mode ≟ 2, A1 + (3, -11), A1 + (6, -9)]) → A70
  70. If(mode ≟ 1, A1 + (0, -7), If[mode ≟ 2, A1 + (4, -11), A1 + (0, -10)]) → A71
  71. If(mode ≟ 1, A1 + (1, -7), If[mode ≟ 2, A1 + (5, -11), A1 + (1, -10)]) → A72
  72. If(mode ≟ 1, A1 + (2, -7), If[mode ≟ 2, A1 + (0, -12), A1 + (2, -10)]) → A73
  73. If(mode ≟ 1, A1 + (3, -7), If[mode ≟ 2, A1 + (1, -12), A1 + (3, -10)]) → A74
  74. If(mode ≟ 1, A1 + (4, -7), If[mode ≟ 2, A1 + (2, -12), A1 + (4, -10)]) → A75
  75. If(mode ≟ 1, A1 + (5, -7), If[mode ≟ 2, A1 + (3, -12), A1 + (5, -10)]) → A76
  76. If(mode ≟ 1, A1 + (6, -7), If[mode ≟ 2, A1 + (4, -12), A1 + (6, -10)]) → A77
  77. If(mode ≟ 1, A1 + (7, -7), If[mode ≟ 2, A1 + (5, -12), A1 + (0, -11)]) → A78
  78. If(mode ≟ 1, A1 + (8, -7), If[mode ≟ 2, A1 + (0, -13), A1 + (1, -11)]) → A79
  79. If(mode ≟ 1, A1 + (9, -7), If[mode ≟ 2, A1 + (1, -13), A1 + (2, -11)]) → A80
  80. If(mode ≟ 1, A1 + (0, -8), If[mode ≟ 2, A1 + (2, -13), A1 + (3, -11)]) → A81
  81. If(mode ≟ 1, A1 + (1, -8), If[mode ≟ 2, A1 + (3, -13), A1 + (4, -11)]) → A82
  82. If(mode ≟ 1, A1 + (2, -8), If[mode ≟ 2, A1 + (4, -13), A1 + (5, -11)]) → A83
  83. If(mode ≟ 1, A1 + (3, -8), If[mode ≟ 2, A1 + (5, -13), A1 + (6, -11)]) → A84
  84. If(mode ≟ 1, A1 + (4, -8), If[mode ≟ 2, A1 + (0, -14), A1 + (0, -12)]) → A85
  85. If(mode ≟ 1, A1 + (5, -8), If[mode ≟ 2, A1 + (1, -14), A1 + (1, -12)]) → A86
  86. If(mode ≟ 1, A1 + (6, -8), If[mode ≟ 2, A1 + (2, -14), A1 + (2, -12)]) → A87
  87. If(mode ≟ 1, A1 + (7, -8), If[mode ≟ 2, A1 + (3, -14), A1 + (3, -12)]) → A88
  88. If(mode ≟ 1, A1 + (8, -8), If[mode ≟ 2, A1 + (4, -14), A1 + (4, -12)]) → A89
  89. If(mode ≟ 1, A1 + (9, -8), If[mode ≟ 2, A1 + (5, -14), A1 + (5, -12)]) → A90
  90. If(mode ≟ 1, A1 + (0, -9), If[mode ≟ 2, A1 + (0, -15), A1 + (6, -12)]) → A91
  91. If(mode ≟ 1, A1 + (1, -9), If[mode ≟ 2, A1 + (1, -15), A1 + (0, -13)]) → A92
  92. If(mode ≟ 1, A1 + (2, -9), If[mode ≟ 2, A1 + (2, -15), A1 + (1, -13)]) → A93
  93. If(mode ≟ 1, A1 + (3, -9), If[mode ≟ 2, A1 + (3, -15), A1 + (2, -13)]) → A94
  94. If(mode ≟ 1, A1 + (4, -9), If[mode ≟ 2, A1 + (4, -15), A1 + (3, -13)]) → A95
  95. If(mode ≟ 1, A1 + (5, -9), If[mode ≟ 2, A1 + (5, -15), A1 + (4, -13)]) → A96
  96. If(mode ≟ 1, A1 + (6, -9), If[mode ≟ 2, A1 + (0, -16), A1 + (5, -13)]) → A97
  97. If(mode ≟ 1, A1 + (7, -9), If[mode ≟ 2, A1 + (1, -16), A1 + (6, -13)]) → A98
  98. If(mode ≟ 1, A1 + (8, -9), If[mode ≟ 2, A1 + (2, -16), A1 + (0, -14)]) → A99
  99. If(mode ≟ 1, A1 + (9, -9), If[mode ≟ 2, A1 + (3, -16), A1 + (1, -14)]) → A100
  100. Polygon({A0, A0 + (1, 0), A0 + (1, 1), A0 + (0, 1)}) → B1
  101. Polygon({A11 - (dx, dy), A11 + (1, 0) - (dx, dy), A11 + (1, 1) - (dx, dy), A11 + (0, 1) - (dx, dy)}) → B11
  102. Polygon({A0 + (1, 0), A0 + (2, 0), A0 + (2, 1), A0 + (1, 1)}) → B2
  103. Polygon({A3 - (dx + 0.2, dy), A3 + (1 - 0.2, 0) - (dx, dy), A3 + (1 - 0.2, 1) - (dx, dy), A3 + (0, 1) - (dx + 0.2, dy)}) → B3
  104. Polygon({A4 - (dx + 0.2, dy), A4 + (1 - 0.2, 0) - (dx, dy), A4 + (1 - 0.2, 1) - (dx, dy), A4 + (0, 1) - (dx + 0.2, dy)}) → B4
  105. Polygon({A12 - (dx, dy), A12 + (1, 0) - (dx, dy), A12 + (1, 1) - (dx, dy), A12 + (0, 1) - (dx, dy)}) → B12
  106. Polygon({A13 - (dx, dy), A13 + (1, 0) - (dx, dy), A13 + (1, 1) - (dx, dy), A13 + (0, 1) - (dx, dy)}) → B13
  107. Polygon({A14 - (dx, dy), A14 + (1, 0) - (dx, dy), A14 + (1, 1) - (dx, dy), A14 + (0, 1) - (dx, dy)}) → B14
  108. Polygon({A15 - (dx, dy), A15 + (1, 0) - (dx, dy), A15 + (1, 1) - (dx, dy), A15 + (0, 1) - (dx, dy)}) → B15
  109. Polygon({A16 - (dx, dy), A16 + (1, 0) - (dx, dy), A16 + (1, 1) - (dx, dy), A16 + (0, 1) - (dx, dy)}) → B16
  110. Polygon({A17 - (dx, dy), A17 + (1, 0) - (dx, dy), A17 + (1, 1) - (dx, dy), A17 + (0, 1) - (dx, dy)}) → B17
  111. Polygon({A18 - (dx, dy), A18 + (1, 0) - (dx, dy), A18 + (1, 1) - (dx, dy), A18 + (0, 1) - (dx, dy)}) → B18
  112. Polygon({A19 - (dx, dy), A19 + (1, 0) - (dx, dy), A19 + (1, 1) - (dx, dy), A19 + (0, 1) - (dx, dy)}) → B19
  113. Polygon({A20 - (dx, dy), A20 + (1, 0) - (dx, dy), A20 + (1, 1) - (dx, dy), A20 + (0, 1) - (dx, dy)}) → B20
  114. Polygon({A21 - (dx, dy), A21 + (1, 0) - (dx, dy), A21 + (1, 1) - (dx, dy), A21 + (0, 1) - (dx, dy)}) → B21
  115. Polygon({A22 - (dx, dy), A22 + (1, 0) - (dx, dy), A22 + (1, 1) - (dx, dy), A22 + (0, 1) - (dx, dy)}) → B22
  116. Polygon({A23 - (dx, dy), A23 + (1, 0) - (dx, dy), A23 + (1, 1) - (dx, dy), A23 + (0, 1) - (dx, dy)}) → B23
  117. Polygon({A24 - (dx, dy), A24 + (1, 0) - (dx, dy), A24 + (1, 1) - (dx, dy), A24 + (0, 1) - (dx, dy)}) → B24
  118. Polygon({A25 - (dx, dy), A25 + (1, 0) - (dx, dy), A25 + (1, 1) - (dx, dy), A25 + (0, 1) - (dx, dy)}) → B25
  119. Polygon({A26 - (dx, dy), A26 + (1, 0) - (dx, dy), A26 + (1, 1) - (dx, dy), A26 + (0, 1) - (dx, dy)}) → B26
  120. Polygon({A27 - (dx, dy), A27 + (1, 0) - (dx, dy), A27 + (1, 1) - (dx, dy), A27 + (0, 1) - (dx, dy)}) → B27
  121. Polygon({A28 - (dx, dy), A28 + (1, 0) - (dx, dy), A28 + (1, 1) - (dx, dy), A28 + (0, 1) - (dx, dy)}) → B28
  122. Polygon({A29 - (dx, dy), A29 + (1, 0) - (dx, dy), A29 + (1, 1) - (dx, dy), A29 + (0, 1) - (dx, dy)}) → B29
  123. Polygon({A30 - (dx, dy), A30 + (1, 0) - (dx, dy), A30 + (1, 1) - (dx, dy), A30 + (0, 1) - (dx, dy)}) → B30
  124. Polygon({A31 - (dx, dy), A31 + (1, 0) - (dx, dy), A31 + (1, 1) - (dx, dy), A31 + (0, 1) - (dx, dy)}) → B31
  125. Polygon({A32 - (dx, dy), A32 + (1, 0) - (dx, dy), A32 + (1, 1) - (dx, dy), A32 + (0, 1) - (dx, dy)}) → B32
  126. Polygon({A33 - (dx, dy), A33 + (1, 0) - (dx, dy), A33 + (1, 1) - (dx, dy), A33 + (0, 1) - (dx, dy)}) → B33
  127. Polygon({A34 - (dx, dy), A34 + (1, 0) - (dx, dy), A34 + (1, 1) - (dx, dy), A34 + (0, 1) - (dx, dy)}) → B34
  128. Polygon({A35 - (dx, dy), A35 + (1, 0) - (dx, dy), A35 + (1, 1) - (dx, dy), A35 + (0, 1) - (dx, dy)}) → B35
  129. Polygon({A36 - (dx, dy), A36 + (1, 0) - (dx, dy), A36 + (1, 1) - (dx, dy), A36 + (0, 1) - (dx, dy)}) → B36
  130. Polygon({A37 - (dx, dy), A37 + (1, 0) - (dx, dy), A37 + (1, 1) - (dx, dy), A37 + (0, 1) - (dx, dy)}) → B37
  131. Polygon({A38 - (dx, dy), A38 + (1, 0) - (dx, dy), A38 + (1, 1) - (dx, dy), A38 + (0, 1) - (dx, dy)}) → B38
  132. Polygon({A39 - (dx, dy), A39 + (1, 0) - (dx, dy), A39 + (1, 1) - (dx, dy), A39 + (0, 1) - (dx, dy)}) → B39
  133. Polygon({A40 - (dx, dy), A40 + (1, 0) - (dx, dy), A40 + (1, 1) - (dx, dy), A40 + (0, 1) - (dx, dy)}) → B40
  134. Polygon({A41 - (dx, dy), A41 + (1, 0) - (dx, dy), A41 + (1, 1) - (dx, dy), A41 + (0, 1) - (dx, dy)}) → B41
  135. Polygon({A42 - (dx, dy), A42 + (1, 0) - (dx, dy), A42 + (1, 1) - (dx, dy), A42 + (0, 1) - (dx, dy)}) → B42
  136. Polygon({A43 - (dx, dy), A43 + (1, 0) - (dx, dy), A43 + (1, 1) - (dx, dy), A43 + (0, 1) - (dx, dy)}) → B43
  137. Polygon({A44 - (dx, dy), A44 + (1, 0) - (dx, dy), A44 + (1, 1) - (dx, dy), A44 + (0, 1) - (dx, dy)}) → B44
  138. Polygon({A45 - (dx, dy), A45 + (1, 0) - (dx, dy), A45 + (1, 1) - (dx, dy), A45 + (0, 1) - (dx, dy)}) → B45
  139. Polygon({A46 - (dx, dy), A46 + (1, 0) - (dx, dy), A46 + (1, 1) - (dx, dy), A46 + (0, 1) - (dx, dy)}) → B46
  140. Polygon({A47 - (dx, dy), A47 + (1, 0) - (dx, dy), A47 + (1, 1) - (dx, dy), A47 + (0, 1) - (dx, dy)}) → B47
  141. Polygon({A48 - (dx, dy), A48 + (1, 0) - (dx, dy), A48 + (1, 1) - (dx, dy), A48 + (0, 1) - (dx, dy)}) → B48
  142. Polygon({A49 - (dx, dy), A49 + (1, 0) - (dx, dy), A49 + (1, 1) - (dx, dy), A49 + (0, 1) - (dx, dy)}) → B49
  143. Polygon({A50 - (dx, dy), A50 + (1, 0) - (dx, dy), A50 + (1, 1) - (dx, dy), A50 + (0, 1) - (dx, dy)}) → B50
  144. Polygon({A51 - (dx, dy), A51 + (1, 0) - (dx, dy), A51 + (1, 1) - (dx, dy), A51 + (0, 1) - (dx, dy)}) → B51
  145. Polygon({A52 - (dx, dy), A52 + (1, 0) - (dx, dy), A52 + (1, 1) - (dx, dy), A52 + (0, 1) - (dx, dy)}) → B52
  146. Polygon({A53 - (dx, dy), A53 + (1, 0) - (dx, dy), A53 + (1, 1) - (dx, dy), A53 + (0, 1) - (dx, dy)}) → B53
  147. Polygon({A54 - (dx, dy), A54 + (1, 0) - (dx, dy), A54 + (1, 1) - (dx, dy), A54 + (0, 1) - (dx, dy)}) → B54
  148. Polygon({A55 - (dx, dy), A55 + (1, 0) - (dx, dy), A55 + (1, 1) - (dx, dy), A55 + (0, 1) - (dx, dy)}) → B55
  149. Polygon({A56 - (dx, dy), A56 + (1, 0) - (dx, dy), A56 + (1, 1) - (dx, dy), A56 + (0, 1) - (dx, dy)}) → B56
  150. Polygon({A57 - (dx, dy), A57 + (1, 0) - (dx, dy), A57 + (1, 1) - (dx, dy), A57 + (0, 1) - (dx, dy)}) → B57
  151. Polygon({A58 - (dx, dy), A58 + (1, 0) - (dx, dy), A58 + (1, 1) - (dx, dy), A58 + (0, 1) - (dx, dy)}) → B58
  152. Polygon({A59 - (dx, dy), A59 + (1, 0) - (dx, dy), A59 + (1, 1) - (dx, dy), A59 + (0, 1) - (dx, dy)}) → B59
  153. Polygon({A60 - (dx, dy), A60 + (1, 0) - (dx, dy), A60 + (1, 1) - (dx, dy), A60 + (0, 1) - (dx, dy)}) → B60
  154. Polygon({A61 - (dx, dy), A61 + (1, 0) - (dx, dy), A61 + (1, 1) - (dx, dy), A61 + (0, 1) - (dx, dy)}) → B61
  155. Polygon({A62 - (dx, dy), A62 + (1, 0) - (dx, dy), A62 + (1, 1) - (dx, dy), A62 + (0, 1) - (dx, dy)}) → B62
  156. Polygon({A63 - (dx, dy), A63 + (1, 0) - (dx, dy), A63 + (1, 1) - (dx, dy), A63 + (0, 1) - (dx, dy)}) → B63
  157. Polygon({A64 - (dx, dy), A64 + (1, 0) - (dx, dy), A64 + (1, 1) - (dx, dy), A64 + (0, 1) - (dx, dy)}) → B64
  158. Polygon({A65 - (dx, dy), A65 + (1, 0) - (dx, dy), A65 + (1, 1) - (dx, dy), A65 + (0, 1) - (dx, dy)}) → B65
  159. Polygon({A66 - (dx, dy), A66 + (1, 0) - (dx, dy), A66 + (1, 1) - (dx, dy), A66 + (0, 1) - (dx, dy)}) → B66
  160. Polygon({A67 - (dx, dy), A67 + (1, 0) - (dx, dy), A67 + (1, 1) - (dx, dy), A67 + (0, 1) - (dx, dy)}) → B67
  161. Polygon({A68 - (dx, dy), A68 + (1, 0) - (dx, dy), A68 + (1, 1) - (dx, dy), A68 + (0, 1) - (dx, dy)}) → B68
  162. Polygon({A69 - (dx, dy), A69 + (1, 0) - (dx, dy), A69 + (1, 1) - (dx, dy), A69 + (0, 1) - (dx, dy)}) → B69
  163. Polygon({A70 - (dx, dy), A70 + (1, 0) - (dx, dy), A70 + (1, 1) - (dx, dy), A70 + (0, 1) - (dx, dy)}) → B70
  164. Polygon({A71 - (dx, dy), A71 + (1, 0) - (dx, dy), A71 + (1, 1) - (dx, dy), A71 + (0, 1) - (dx, dy)}) → B71
  165. Polygon({A72 - (dx, dy), A72 + (1, 0) - (dx, dy), A72 + (1, 1) - (dx, dy), A72 + (0, 1) - (dx, dy)}) → B72
  166. Polygon({A73 - (dx, dy), A73 + (1, 0) - (dx, dy), A73 + (1, 1) - (dx, dy), A73 + (0, 1) - (dx, dy)}) → B73
  167. Polygon({A74 - (dx, dy), A74 + (1, 0) - (dx, dy), A74 + (1, 1) - (dx, dy), A74 + (0, 1) - (dx, dy)}) → B74
  168. Polygon({A75 - (dx, dy), A75 + (1, 0) - (dx, dy), A75 + (1, 1) - (dx, dy), A75 + (0, 1) - (dx, dy)}) → B75
  169. Polygon({A76 - (dx, dy), A76 + (1, 0) - (dx, dy), A76 + (1, 1) - (dx, dy), A76 + (0, 1) - (dx, dy)}) → B76
  170. Polygon({A77 - (dx, dy), A77 + (1, 0) - (dx, dy), A77 + (1, 1) - (dx, dy), A77 + (0, 1) - (dx, dy)}) → B77
  171. Polygon({A78 - (dx, dy), A78 + (1, 0) - (dx, dy), A78 + (1, 1) - (dx, dy), A78 + (0, 1) - (dx, dy)}) → B78
  172. Polygon({A79 - (dx, dy), A79 + (1, 0) - (dx, dy), A79 + (1, 1) - (dx, dy), A79 + (0, 1) - (dx, dy)}) → B79
  173. Polygon({A80 - (dx, dy), A80 + (1, 0) - (dx, dy), A80 + (1, 1) - (dx, dy), A80 + (0, 1) - (dx, dy)}) → B80
  174. Polygon({A81 - (dx, dy), A81 + (1, 0) - (dx, dy), A81 + (1, 1) - (dx, dy), A81 + (0, 1) - (dx, dy)}) → B81
  175. Polygon({A82 - (dx, dy), A82 + (1, 0) - (dx, dy), A82 + (1, 1) - (dx, dy), A82 + (0, 1) - (dx, dy)}) → B82
  176. Polygon({A83 - (dx, dy), A83 + (1, 0) - (dx, dy), A83 + (1, 1) - (dx, dy), A83 + (0, 1) - (dx, dy)}) → B83
  177. Polygon({A84 - (dx, dy), A84 + (1, 0) - (dx, dy), A84 + (1, 1) - (dx, dy), A84 + (0, 1) - (dx, dy)}) → B84
  178. Polygon({A85 - (dx, dy), A85 + (1, 0) - (dx, dy), A85 + (1, 1) - (dx, dy), A85 + (0, 1) - (dx, dy)}) → B85
  179. Polygon({A86 - (dx, dy), A86 + (1, 0) - (dx, dy), A86 + (1, 1) - (dx, dy), A86 + (0, 1) - (dx, dy)}) → B86
  180. Polygon({A87 - (dx, dy), A87 + (1, 0) - (dx, dy), A87 + (1, 1) - (dx, dy), A87 + (0, 1) - (dx, dy)}) → B87
  181. Polygon({A88 - (dx, dy), A88 + (1, 0) - (dx, dy), A88 + (1, 1) - (dx, dy), A88 + (0, 1) - (dx, dy)}) → B88
  182. Polygon({A89 - (dx, dy), A89 + (1, 0) - (dx, dy), A89 + (1, 1) - (dx, dy), A89 + (0, 1) - (dx, dy)}) → B89
  183. Polygon({A90 - (dx, dy), A90 + (1, 0) - (dx, dy), A90 + (1, 1) - (dx, dy), A90 + (0, 1) - (dx, dy)}) → B90
  184. Polygon({A91 - (dx, dy), A91 + (1, 0) - (dx, dy), A91 + (1, 1) - (dx, dy), A91 + (0, 1) - (dx, dy)}) → B91
  185. Polygon({A92 - (dx, dy), A92 + (1, 0) - (dx, dy), A92 + (1, 1) - (dx, dy), A92 + (0, 1) - (dx, dy)}) → B92
  186. Polygon({A93 - (dx, dy), A93 + (1, 0) - (dx, dy), A93 + (1, 1) - (dx, dy), A93 + (0, 1) - (dx, dy)}) → B93
  187. Polygon({A94 - (dx, dy), A94 + (1, 0) - (dx, dy), A94 + (1, 1) - (dx, dy), A94 + (0, 1) - (dx, dy)}) → B94
  188. Polygon({A95 - (dx, dy), A95 + (1, 0) - (dx, dy), A95 + (1, 1) - (dx, dy), A95 + (0, 1) - (dx, dy)}) → B95
  189. Polygon({A96 - (dx, dy), A96 + (1, 0) - (dx, dy), A96 + (1, 1) - (dx, dy), A96 + (0, 1) - (dx, dy)}) → B96
  190. Polygon({A97 - (dx, dy), A97 + (1, 0) - (dx, dy), A97 + (1, 1) - (dx, dy), A97 + (0, 1) - (dx, dy)}) → B97
  191. Polygon({A98 - (dx, dy), A98 + (1, 0) - (dx, dy), A98 + (1, 1) - (dx, dy), A98 + (0, 1) - (dx, dy)}) → B98
  192. Polygon({A99 - (dx, dy), A99 + (1, 0) - (dx, dy), A99 + (1, 1) - (dx, dy), A99 + (0, 1) - (dx, dy)}) → B99
  193. Polygon({A100 - (dx, dy), A100 + (1, 0) - (dx, dy), A100 + (1, 1) - (dx, dy), A100 + (0, 1) - (dx, dy)}) → B100
  194. Polygon({A5 - (dx + 0.2, dy), A5 + (1 - 0.2, 0) - (dx, dy), A5 + (1 - 0.2, 1) - (dx, dy), A5 + (0, 1) - (dx + 0.2, dy)}) → B5
  195. Polygon({A6 - (dx + 0.2, dy), A6 + (1 - 0.2, 0) - (dx, dy), A6 + (1 - 0.2, 1) - (dx, dy), A6 + (0, 1) - (dx + 0.2, dy)}) → B6
  196. Polygon({A7 - (dx, dy), A7 + (1, 0) - (dx, dy), A7 + (1, 1) - (dx, dy), A7 + (0, 1) - (dx, dy)}) → B7
  197. Polygon({A8 - (dx, dy), A8 + (1, 0) - (dx, dy), A8 + (1, 1) - (dx, dy), A8 + (0, 1) - (dx, dy)}) → B8
  198. Polygon({A9 - (dx, dy), A9 + (1, 0) - (dx, dy), A9 + (1, 1) - (dx, dy), A9 + (0, 1) - (dx, dy)}) → B9
  199. Polygon({A10 - (dx, dy), A10 + (1, 0) - (dx, dy), A10 + (1, 1) - (dx, dy), A10 + (0, 1) - (dx, dy)}) → B10
  200. Sequence(Segment[(0, i), (10, i)], i, 0, 10) → L2

AI 绘图提示语参考

绘制一个用于展示埃拉托斯特尼筛法的数字网格图。网格由水平和垂直线段构成，形成多行多列的矩形单元格，覆盖从负坐标到正坐标的区域。图中包含一个可调节的模式滑块，用于切换不同的筛选阶段。根据模式的不同，一系列标记点会以特定规律移动，形成不同的排列路径，模拟筛选中数字的标记过程。网格中应包含数字标签，用于标识每个单元格对应的数值。整体布局清晰，便于观察质数与合数的分布规律。
以上提示语为根据原始绘图命令整理而来，仅供参考。