
theorem
  4273 is prime
proof
  now
    4273 = 2*2136 + 1; hence not 2 divides 4273 by NAT_4:9;
    4273 = 3*1424 + 1; hence not 3 divides 4273 by NAT_4:9;
    4273 = 5*854 + 3; hence not 5 divides 4273 by NAT_4:9;
    4273 = 7*610 + 3; hence not 7 divides 4273 by NAT_4:9;
    4273 = 11*388 + 5; hence not 11 divides 4273 by NAT_4:9;
    4273 = 13*328 + 9; hence not 13 divides 4273 by NAT_4:9;
    4273 = 17*251 + 6; hence not 17 divides 4273 by NAT_4:9;
    4273 = 19*224 + 17; hence not 19 divides 4273 by NAT_4:9;
    4273 = 23*185 + 18; hence not 23 divides 4273 by NAT_4:9;
    4273 = 29*147 + 10; hence not 29 divides 4273 by NAT_4:9;
    4273 = 31*137 + 26; hence not 31 divides 4273 by NAT_4:9;
    4273 = 37*115 + 18; hence not 37 divides 4273 by NAT_4:9;
    4273 = 41*104 + 9; hence not 41 divides 4273 by NAT_4:9;
    4273 = 43*99 + 16; hence not 43 divides 4273 by NAT_4:9;
    4273 = 47*90 + 43; hence not 47 divides 4273 by NAT_4:9;
    4273 = 53*80 + 33; hence not 53 divides 4273 by NAT_4:9;
    4273 = 59*72 + 25; hence not 59 divides 4273 by NAT_4:9;
    4273 = 61*70 + 3; hence not 61 divides 4273 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4273 & n is prime
  holds not n divides 4273 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
