
theorem
  6277 is prime
proof
  now
    6277 = 2*3138 + 1; hence not 2 divides 6277 by NAT_4:9;
    6277 = 3*2092 + 1; hence not 3 divides 6277 by NAT_4:9;
    6277 = 5*1255 + 2; hence not 5 divides 6277 by NAT_4:9;
    6277 = 7*896 + 5; hence not 7 divides 6277 by NAT_4:9;
    6277 = 11*570 + 7; hence not 11 divides 6277 by NAT_4:9;
    6277 = 13*482 + 11; hence not 13 divides 6277 by NAT_4:9;
    6277 = 17*369 + 4; hence not 17 divides 6277 by NAT_4:9;
    6277 = 19*330 + 7; hence not 19 divides 6277 by NAT_4:9;
    6277 = 23*272 + 21; hence not 23 divides 6277 by NAT_4:9;
    6277 = 29*216 + 13; hence not 29 divides 6277 by NAT_4:9;
    6277 = 31*202 + 15; hence not 31 divides 6277 by NAT_4:9;
    6277 = 37*169 + 24; hence not 37 divides 6277 by NAT_4:9;
    6277 = 41*153 + 4; hence not 41 divides 6277 by NAT_4:9;
    6277 = 43*145 + 42; hence not 43 divides 6277 by NAT_4:9;
    6277 = 47*133 + 26; hence not 47 divides 6277 by NAT_4:9;
    6277 = 53*118 + 23; hence not 53 divides 6277 by NAT_4:9;
    6277 = 59*106 + 23; hence not 59 divides 6277 by NAT_4:9;
    6277 = 61*102 + 55; hence not 61 divides 6277 by NAT_4:9;
    6277 = 67*93 + 46; hence not 67 divides 6277 by NAT_4:9;
    6277 = 71*88 + 29; hence not 71 divides 6277 by NAT_4:9;
    6277 = 73*85 + 72; hence not 73 divides 6277 by NAT_4:9;
    6277 = 79*79 + 36; hence not 79 divides 6277 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6277 & n is prime
  holds not n divides 6277 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
