
theorem
  6029 is prime
proof
  now
    6029 = 2*3014 + 1; hence not 2 divides 6029 by NAT_4:9;
    6029 = 3*2009 + 2; hence not 3 divides 6029 by NAT_4:9;
    6029 = 5*1205 + 4; hence not 5 divides 6029 by NAT_4:9;
    6029 = 7*861 + 2; hence not 7 divides 6029 by NAT_4:9;
    6029 = 11*548 + 1; hence not 11 divides 6029 by NAT_4:9;
    6029 = 13*463 + 10; hence not 13 divides 6029 by NAT_4:9;
    6029 = 17*354 + 11; hence not 17 divides 6029 by NAT_4:9;
    6029 = 19*317 + 6; hence not 19 divides 6029 by NAT_4:9;
    6029 = 23*262 + 3; hence not 23 divides 6029 by NAT_4:9;
    6029 = 29*207 + 26; hence not 29 divides 6029 by NAT_4:9;
    6029 = 31*194 + 15; hence not 31 divides 6029 by NAT_4:9;
    6029 = 37*162 + 35; hence not 37 divides 6029 by NAT_4:9;
    6029 = 41*147 + 2; hence not 41 divides 6029 by NAT_4:9;
    6029 = 43*140 + 9; hence not 43 divides 6029 by NAT_4:9;
    6029 = 47*128 + 13; hence not 47 divides 6029 by NAT_4:9;
    6029 = 53*113 + 40; hence not 53 divides 6029 by NAT_4:9;
    6029 = 59*102 + 11; hence not 59 divides 6029 by NAT_4:9;
    6029 = 61*98 + 51; hence not 61 divides 6029 by NAT_4:9;
    6029 = 67*89 + 66; hence not 67 divides 6029 by NAT_4:9;
    6029 = 71*84 + 65; hence not 71 divides 6029 by NAT_4:9;
    6029 = 73*82 + 43; hence not 73 divides 6029 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6029 & n is prime
  holds not n divides 6029 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
