
theorem
  1259 is prime
proof
  now
    1259 = 2*629 + 1; hence not 2 divides 1259 by NAT_4:9;
    1259 = 3*419 + 2; hence not 3 divides 1259 by NAT_4:9;
    1259 = 5*251 + 4; hence not 5 divides 1259 by NAT_4:9;
    1259 = 7*179 + 6; hence not 7 divides 1259 by NAT_4:9;
    1259 = 11*114 + 5; hence not 11 divides 1259 by NAT_4:9;
    1259 = 13*96 + 11; hence not 13 divides 1259 by NAT_4:9;
    1259 = 17*74 + 1; hence not 17 divides 1259 by NAT_4:9;
    1259 = 19*66 + 5; hence not 19 divides 1259 by NAT_4:9;
    1259 = 23*54 + 17; hence not 23 divides 1259 by NAT_4:9;
    1259 = 29*43 + 12; hence not 29 divides 1259 by NAT_4:9;
    1259 = 31*40 + 19; hence not 31 divides 1259 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1259 & n is prime
  holds not n divides 1259 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
