
theorem
  6037 is prime
proof
  now
    6037 = 2*3018 + 1; hence not 2 divides 6037 by NAT_4:9;
    6037 = 3*2012 + 1; hence not 3 divides 6037 by NAT_4:9;
    6037 = 5*1207 + 2; hence not 5 divides 6037 by NAT_4:9;
    6037 = 7*862 + 3; hence not 7 divides 6037 by NAT_4:9;
    6037 = 11*548 + 9; hence not 11 divides 6037 by NAT_4:9;
    6037 = 13*464 + 5; hence not 13 divides 6037 by NAT_4:9;
    6037 = 17*355 + 2; hence not 17 divides 6037 by NAT_4:9;
    6037 = 19*317 + 14; hence not 19 divides 6037 by NAT_4:9;
    6037 = 23*262 + 11; hence not 23 divides 6037 by NAT_4:9;
    6037 = 29*208 + 5; hence not 29 divides 6037 by NAT_4:9;
    6037 = 31*194 + 23; hence not 31 divides 6037 by NAT_4:9;
    6037 = 37*163 + 6; hence not 37 divides 6037 by NAT_4:9;
    6037 = 41*147 + 10; hence not 41 divides 6037 by NAT_4:9;
    6037 = 43*140 + 17; hence not 43 divides 6037 by NAT_4:9;
    6037 = 47*128 + 21; hence not 47 divides 6037 by NAT_4:9;
    6037 = 53*113 + 48; hence not 53 divides 6037 by NAT_4:9;
    6037 = 59*102 + 19; hence not 59 divides 6037 by NAT_4:9;
    6037 = 61*98 + 59; hence not 61 divides 6037 by NAT_4:9;
    6037 = 67*90 + 7; hence not 67 divides 6037 by NAT_4:9;
    6037 = 71*85 + 2; hence not 71 divides 6037 by NAT_4:9;
    6037 = 73*82 + 51; hence not 73 divides 6037 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6037 & n is prime
  holds not n divides 6037 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
