
theorem
  7211 is prime
proof
  now
    7211 = 2*3605 + 1; hence not 2 divides 7211 by NAT_4:9;
    7211 = 3*2403 + 2; hence not 3 divides 7211 by NAT_4:9;
    7211 = 5*1442 + 1; hence not 5 divides 7211 by NAT_4:9;
    7211 = 7*1030 + 1; hence not 7 divides 7211 by NAT_4:9;
    7211 = 11*655 + 6; hence not 11 divides 7211 by NAT_4:9;
    7211 = 13*554 + 9; hence not 13 divides 7211 by NAT_4:9;
    7211 = 17*424 + 3; hence not 17 divides 7211 by NAT_4:9;
    7211 = 19*379 + 10; hence not 19 divides 7211 by NAT_4:9;
    7211 = 23*313 + 12; hence not 23 divides 7211 by NAT_4:9;
    7211 = 29*248 + 19; hence not 29 divides 7211 by NAT_4:9;
    7211 = 31*232 + 19; hence not 31 divides 7211 by NAT_4:9;
    7211 = 37*194 + 33; hence not 37 divides 7211 by NAT_4:9;
    7211 = 41*175 + 36; hence not 41 divides 7211 by NAT_4:9;
    7211 = 43*167 + 30; hence not 43 divides 7211 by NAT_4:9;
    7211 = 47*153 + 20; hence not 47 divides 7211 by NAT_4:9;
    7211 = 53*136 + 3; hence not 53 divides 7211 by NAT_4:9;
    7211 = 59*122 + 13; hence not 59 divides 7211 by NAT_4:9;
    7211 = 61*118 + 13; hence not 61 divides 7211 by NAT_4:9;
    7211 = 67*107 + 42; hence not 67 divides 7211 by NAT_4:9;
    7211 = 71*101 + 40; hence not 71 divides 7211 by NAT_4:9;
    7211 = 73*98 + 57; hence not 73 divides 7211 by NAT_4:9;
    7211 = 79*91 + 22; hence not 79 divides 7211 by NAT_4:9;
    7211 = 83*86 + 73; hence not 83 divides 7211 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7211 & n is prime
  holds not n divides 7211 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
