
theorem
  7253 is prime
proof
  now
    7253 = 2*3626 + 1; hence not 2 divides 7253 by NAT_4:9;
    7253 = 3*2417 + 2; hence not 3 divides 7253 by NAT_4:9;
    7253 = 5*1450 + 3; hence not 5 divides 7253 by NAT_4:9;
    7253 = 7*1036 + 1; hence not 7 divides 7253 by NAT_4:9;
    7253 = 11*659 + 4; hence not 11 divides 7253 by NAT_4:9;
    7253 = 13*557 + 12; hence not 13 divides 7253 by NAT_4:9;
    7253 = 17*426 + 11; hence not 17 divides 7253 by NAT_4:9;
    7253 = 19*381 + 14; hence not 19 divides 7253 by NAT_4:9;
    7253 = 23*315 + 8; hence not 23 divides 7253 by NAT_4:9;
    7253 = 29*250 + 3; hence not 29 divides 7253 by NAT_4:9;
    7253 = 31*233 + 30; hence not 31 divides 7253 by NAT_4:9;
    7253 = 37*196 + 1; hence not 37 divides 7253 by NAT_4:9;
    7253 = 41*176 + 37; hence not 41 divides 7253 by NAT_4:9;
    7253 = 43*168 + 29; hence not 43 divides 7253 by NAT_4:9;
    7253 = 47*154 + 15; hence not 47 divides 7253 by NAT_4:9;
    7253 = 53*136 + 45; hence not 53 divides 7253 by NAT_4:9;
    7253 = 59*122 + 55; hence not 59 divides 7253 by NAT_4:9;
    7253 = 61*118 + 55; hence not 61 divides 7253 by NAT_4:9;
    7253 = 67*108 + 17; hence not 67 divides 7253 by NAT_4:9;
    7253 = 71*102 + 11; hence not 71 divides 7253 by NAT_4:9;
    7253 = 73*99 + 26; hence not 73 divides 7253 by NAT_4:9;
    7253 = 79*91 + 64; hence not 79 divides 7253 by NAT_4:9;
    7253 = 83*87 + 32; hence not 83 divides 7253 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7253 & n is prime
  holds not n divides 7253 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
