
theorem
  7013 is prime
proof
  now
    7013 = 2*3506 + 1; hence not 2 divides 7013 by NAT_4:9;
    7013 = 3*2337 + 2; hence not 3 divides 7013 by NAT_4:9;
    7013 = 5*1402 + 3; hence not 5 divides 7013 by NAT_4:9;
    7013 = 7*1001 + 6; hence not 7 divides 7013 by NAT_4:9;
    7013 = 11*637 + 6; hence not 11 divides 7013 by NAT_4:9;
    7013 = 13*539 + 6; hence not 13 divides 7013 by NAT_4:9;
    7013 = 17*412 + 9; hence not 17 divides 7013 by NAT_4:9;
    7013 = 19*369 + 2; hence not 19 divides 7013 by NAT_4:9;
    7013 = 23*304 + 21; hence not 23 divides 7013 by NAT_4:9;
    7013 = 29*241 + 24; hence not 29 divides 7013 by NAT_4:9;
    7013 = 31*226 + 7; hence not 31 divides 7013 by NAT_4:9;
    7013 = 37*189 + 20; hence not 37 divides 7013 by NAT_4:9;
    7013 = 41*171 + 2; hence not 41 divides 7013 by NAT_4:9;
    7013 = 43*163 + 4; hence not 43 divides 7013 by NAT_4:9;
    7013 = 47*149 + 10; hence not 47 divides 7013 by NAT_4:9;
    7013 = 53*132 + 17; hence not 53 divides 7013 by NAT_4:9;
    7013 = 59*118 + 51; hence not 59 divides 7013 by NAT_4:9;
    7013 = 61*114 + 59; hence not 61 divides 7013 by NAT_4:9;
    7013 = 67*104 + 45; hence not 67 divides 7013 by NAT_4:9;
    7013 = 71*98 + 55; hence not 71 divides 7013 by NAT_4:9;
    7013 = 73*96 + 5; hence not 73 divides 7013 by NAT_4:9;
    7013 = 79*88 + 61; hence not 79 divides 7013 by NAT_4:9;
    7013 = 83*84 + 41; hence not 83 divides 7013 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7013 & n is prime
  holds not n divides 7013 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
