
theorem
  6287 is prime
proof
  now
    6287 = 2*3143 + 1; hence not 2 divides 6287 by NAT_4:9;
    6287 = 3*2095 + 2; hence not 3 divides 6287 by NAT_4:9;
    6287 = 5*1257 + 2; hence not 5 divides 6287 by NAT_4:9;
    6287 = 7*898 + 1; hence not 7 divides 6287 by NAT_4:9;
    6287 = 11*571 + 6; hence not 11 divides 6287 by NAT_4:9;
    6287 = 13*483 + 8; hence not 13 divides 6287 by NAT_4:9;
    6287 = 17*369 + 14; hence not 17 divides 6287 by NAT_4:9;
    6287 = 19*330 + 17; hence not 19 divides 6287 by NAT_4:9;
    6287 = 23*273 + 8; hence not 23 divides 6287 by NAT_4:9;
    6287 = 29*216 + 23; hence not 29 divides 6287 by NAT_4:9;
    6287 = 31*202 + 25; hence not 31 divides 6287 by NAT_4:9;
    6287 = 37*169 + 34; hence not 37 divides 6287 by NAT_4:9;
    6287 = 41*153 + 14; hence not 41 divides 6287 by NAT_4:9;
    6287 = 43*146 + 9; hence not 43 divides 6287 by NAT_4:9;
    6287 = 47*133 + 36; hence not 47 divides 6287 by NAT_4:9;
    6287 = 53*118 + 33; hence not 53 divides 6287 by NAT_4:9;
    6287 = 59*106 + 33; hence not 59 divides 6287 by NAT_4:9;
    6287 = 61*103 + 4; hence not 61 divides 6287 by NAT_4:9;
    6287 = 67*93 + 56; hence not 67 divides 6287 by NAT_4:9;
    6287 = 71*88 + 39; hence not 71 divides 6287 by NAT_4:9;
    6287 = 73*86 + 9; hence not 73 divides 6287 by NAT_4:9;
    6287 = 79*79 + 46; hence not 79 divides 6287 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6287 & n is prime
  holds not n divides 6287 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
