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Numbers answer

  • 14, 9
    142 - 92 = 196 - 81 = 115
  • 11, 2
    112 -22 = 121 - 4 = 117
  • 12, 5
    122 - 52 = 144 - 25 = 119
  • 11, 0
    112 - 02 = 121 - 0 = 121
  • 22, 19
    222 - 192 = 484 - 361 = 123
  • 15, 10
    152 - 102 = 225 - 100 = 125
  • 64, 63
    642 - 632 = 4096 - 3969 = 127
Of course, these were the smallest number pairs for each point in the sequence; and I used odd numbers only. The full sequence from 115 to 127 would be
  • 115: 14, 9; 58, 57
  • 116: 16½, 12½; 30, 28; 58½, 57½
  • 117: 11, 2; 21, 18; 59, 58
  • 118: 30½, 28½; 59½, 58½
  • 119: 12, 5; 60, 59
  • 120: 11, 1; 11½, 3½; 13, 7; 14½, 9½; 17, 13; 21½, 18½; 31, 29; 60½, 59½
  • 121: 11, 0; 61, 60
  • 122: 31½, 29½; 61½, 60½
  • 123: 22, 19; 62, 61
  • 124: 17½, 13½; 32, 30; 62½, 61½
  • 125: 15, 10; 63, 62
  • 126: 11½, 2½; 12½, 5½; 13½, 7½; 22½, 19½; 32½, 30½; 63½, 62½
  • 127: 64, 63
113 and 127 are the lowest pair of consecutive prime numbers whose difference is 14.

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