
theorem
  7213 is prime
proof
  now
    7213 = 2*3606 + 1; hence not 2 divides 7213 by NAT_4:9;
    7213 = 3*2404 + 1; hence not 3 divides 7213 by NAT_4:9;
    7213 = 5*1442 + 3; hence not 5 divides 7213 by NAT_4:9;
    7213 = 7*1030 + 3; hence not 7 divides 7213 by NAT_4:9;
    7213 = 11*655 + 8; hence not 11 divides 7213 by NAT_4:9;
    7213 = 13*554 + 11; hence not 13 divides 7213 by NAT_4:9;
    7213 = 17*424 + 5; hence not 17 divides 7213 by NAT_4:9;
    7213 = 19*379 + 12; hence not 19 divides 7213 by NAT_4:9;
    7213 = 23*313 + 14; hence not 23 divides 7213 by NAT_4:9;
    7213 = 29*248 + 21; hence not 29 divides 7213 by NAT_4:9;
    7213 = 31*232 + 21; hence not 31 divides 7213 by NAT_4:9;
    7213 = 37*194 + 35; hence not 37 divides 7213 by NAT_4:9;
    7213 = 41*175 + 38; hence not 41 divides 7213 by NAT_4:9;
    7213 = 43*167 + 32; hence not 43 divides 7213 by NAT_4:9;
    7213 = 47*153 + 22; hence not 47 divides 7213 by NAT_4:9;
    7213 = 53*136 + 5; hence not 53 divides 7213 by NAT_4:9;
    7213 = 59*122 + 15; hence not 59 divides 7213 by NAT_4:9;
    7213 = 61*118 + 15; hence not 61 divides 7213 by NAT_4:9;
    7213 = 67*107 + 44; hence not 67 divides 7213 by NAT_4:9;
    7213 = 71*101 + 42; hence not 71 divides 7213 by NAT_4:9;
    7213 = 73*98 + 59; hence not 73 divides 7213 by NAT_4:9;
    7213 = 79*91 + 24; hence not 79 divides 7213 by NAT_4:9;
    7213 = 83*86 + 75; hence not 83 divides 7213 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7213 & n is prime
  holds not n divides 7213 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
