
theorem
  5273 is prime
proof
  now
    5273 = 2*2636 + 1; hence not 2 divides 5273 by NAT_4:9;
    5273 = 3*1757 + 2; hence not 3 divides 5273 by NAT_4:9;
    5273 = 5*1054 + 3; hence not 5 divides 5273 by NAT_4:9;
    5273 = 7*753 + 2; hence not 7 divides 5273 by NAT_4:9;
    5273 = 11*479 + 4; hence not 11 divides 5273 by NAT_4:9;
    5273 = 13*405 + 8; hence not 13 divides 5273 by NAT_4:9;
    5273 = 17*310 + 3; hence not 17 divides 5273 by NAT_4:9;
    5273 = 19*277 + 10; hence not 19 divides 5273 by NAT_4:9;
    5273 = 23*229 + 6; hence not 23 divides 5273 by NAT_4:9;
    5273 = 29*181 + 24; hence not 29 divides 5273 by NAT_4:9;
    5273 = 31*170 + 3; hence not 31 divides 5273 by NAT_4:9;
    5273 = 37*142 + 19; hence not 37 divides 5273 by NAT_4:9;
    5273 = 41*128 + 25; hence not 41 divides 5273 by NAT_4:9;
    5273 = 43*122 + 27; hence not 43 divides 5273 by NAT_4:9;
    5273 = 47*112 + 9; hence not 47 divides 5273 by NAT_4:9;
    5273 = 53*99 + 26; hence not 53 divides 5273 by NAT_4:9;
    5273 = 59*89 + 22; hence not 59 divides 5273 by NAT_4:9;
    5273 = 61*86 + 27; hence not 61 divides 5273 by NAT_4:9;
    5273 = 67*78 + 47; hence not 67 divides 5273 by NAT_4:9;
    5273 = 71*74 + 19; hence not 71 divides 5273 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5273 & n is prime
  holds not n divides 5273 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
