
theorem
  6373 is prime
proof
  now
    6373 = 2*3186 + 1; hence not 2 divides 6373 by NAT_4:9;
    6373 = 3*2124 + 1; hence not 3 divides 6373 by NAT_4:9;
    6373 = 5*1274 + 3; hence not 5 divides 6373 by NAT_4:9;
    6373 = 7*910 + 3; hence not 7 divides 6373 by NAT_4:9;
    6373 = 11*579 + 4; hence not 11 divides 6373 by NAT_4:9;
    6373 = 13*490 + 3; hence not 13 divides 6373 by NAT_4:9;
    6373 = 17*374 + 15; hence not 17 divides 6373 by NAT_4:9;
    6373 = 19*335 + 8; hence not 19 divides 6373 by NAT_4:9;
    6373 = 23*277 + 2; hence not 23 divides 6373 by NAT_4:9;
    6373 = 29*219 + 22; hence not 29 divides 6373 by NAT_4:9;
    6373 = 31*205 + 18; hence not 31 divides 6373 by NAT_4:9;
    6373 = 37*172 + 9; hence not 37 divides 6373 by NAT_4:9;
    6373 = 41*155 + 18; hence not 41 divides 6373 by NAT_4:9;
    6373 = 43*148 + 9; hence not 43 divides 6373 by NAT_4:9;
    6373 = 47*135 + 28; hence not 47 divides 6373 by NAT_4:9;
    6373 = 53*120 + 13; hence not 53 divides 6373 by NAT_4:9;
    6373 = 59*108 + 1; hence not 59 divides 6373 by NAT_4:9;
    6373 = 61*104 + 29; hence not 61 divides 6373 by NAT_4:9;
    6373 = 67*95 + 8; hence not 67 divides 6373 by NAT_4:9;
    6373 = 71*89 + 54; hence not 71 divides 6373 by NAT_4:9;
    6373 = 73*87 + 22; hence not 73 divides 6373 by NAT_4:9;
    6373 = 79*80 + 53; hence not 79 divides 6373 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6373 & n is prime
  holds not n divides 6373 by XPRIMET1:44;
  hence thesis by NAT_4:14;
end;
