
theorem
  1283 is prime
proof
  now
    1283 = 2*641 + 1; hence not 2 divides 1283 by NAT_4:9;
    1283 = 3*427 + 2; hence not 3 divides 1283 by NAT_4:9;
    1283 = 5*256 + 3; hence not 5 divides 1283 by NAT_4:9;
    1283 = 7*183 + 2; hence not 7 divides 1283 by NAT_4:9;
    1283 = 11*116 + 7; hence not 11 divides 1283 by NAT_4:9;
    1283 = 13*98 + 9; hence not 13 divides 1283 by NAT_4:9;
    1283 = 17*75 + 8; hence not 17 divides 1283 by NAT_4:9;
    1283 = 19*67 + 10; hence not 19 divides 1283 by NAT_4:9;
    1283 = 23*55 + 18; hence not 23 divides 1283 by NAT_4:9;
    1283 = 29*44 + 7; hence not 29 divides 1283 by NAT_4:9;
    1283 = 31*41 + 12; hence not 31 divides 1283 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1283 & n is prime
  holds not n divides 1283 by XPRIMET1:22;
  hence thesis by NAT_4:14;
