
theorem
  3253 is prime
proof
  now
    3253 = 2*1626 + 1; hence not 2 divides 3253 by NAT_4:9;
    3253 = 3*1084 + 1; hence not 3 divides 3253 by NAT_4:9;
    3253 = 5*650 + 3; hence not 5 divides 3253 by NAT_4:9;
    3253 = 7*464 + 5; hence not 7 divides 3253 by NAT_4:9;
    3253 = 11*295 + 8; hence not 11 divides 3253 by NAT_4:9;
    3253 = 13*250 + 3; hence not 13 divides 3253 by NAT_4:9;
    3253 = 17*191 + 6; hence not 17 divides 3253 by NAT_4:9;
    3253 = 19*171 + 4; hence not 19 divides 3253 by NAT_4:9;
    3253 = 23*141 + 10; hence not 23 divides 3253 by NAT_4:9;
    3253 = 29*112 + 5; hence not 29 divides 3253 by NAT_4:9;
    3253 = 31*104 + 29; hence not 31 divides 3253 by NAT_4:9;
    3253 = 37*87 + 34; hence not 37 divides 3253 by NAT_4:9;
    3253 = 41*79 + 14; hence not 41 divides 3253 by NAT_4:9;
    3253 = 43*75 + 28; hence not 43 divides 3253 by NAT_4:9;
    3253 = 47*69 + 10; hence not 47 divides 3253 by NAT_4:9;
    3253 = 53*61 + 20; hence not 53 divides 3253 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3253 & n is prime
  holds not n divides 3253 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
