
theorem
  3251 is prime
proof
  now
    3251 = 2*1625 + 1; hence not 2 divides 3251 by NAT_4:9;
    3251 = 3*1083 + 2; hence not 3 divides 3251 by NAT_4:9;
    3251 = 5*650 + 1; hence not 5 divides 3251 by NAT_4:9;
    3251 = 7*464 + 3; hence not 7 divides 3251 by NAT_4:9;
    3251 = 11*295 + 6; hence not 11 divides 3251 by NAT_4:9;
    3251 = 13*250 + 1; hence not 13 divides 3251 by NAT_4:9;
    3251 = 17*191 + 4; hence not 17 divides 3251 by NAT_4:9;
    3251 = 19*171 + 2; hence not 19 divides 3251 by NAT_4:9;
    3251 = 23*141 + 8; hence not 23 divides 3251 by NAT_4:9;
    3251 = 29*112 + 3; hence not 29 divides 3251 by NAT_4:9;
    3251 = 31*104 + 27; hence not 31 divides 3251 by NAT_4:9;
    3251 = 37*87 + 32; hence not 37 divides 3251 by NAT_4:9;
    3251 = 41*79 + 12; hence not 41 divides 3251 by NAT_4:9;
    3251 = 43*75 + 26; hence not 43 divides 3251 by NAT_4:9;
    3251 = 47*69 + 8; hence not 47 divides 3251 by NAT_4:9;
    3251 = 53*61 + 18; hence not 53 divides 3251 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3251 & n is prime
  holds not n divides 3251 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
