
theorem
  1279 is prime
proof
  now
    1279 = 2*639 + 1; hence not 2 divides 1279 by NAT_4:9;
    1279 = 3*426 + 1; hence not 3 divides 1279 by NAT_4:9;
    1279 = 5*255 + 4; hence not 5 divides 1279 by NAT_4:9;
    1279 = 7*182 + 5; hence not 7 divides 1279 by NAT_4:9;
    1279 = 11*116 + 3; hence not 11 divides 1279 by NAT_4:9;
    1279 = 13*98 + 5; hence not 13 divides 1279 by NAT_4:9;
    1279 = 17*75 + 4; hence not 17 divides 1279 by NAT_4:9;
    1279 = 19*67 + 6; hence not 19 divides 1279 by NAT_4:9;
    1279 = 23*55 + 14; hence not 23 divides 1279 by NAT_4:9;
    1279 = 29*44 + 3; hence not 29 divides 1279 by NAT_4:9;
    1279 = 31*41 + 8; hence not 31 divides 1279 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1279 & n is prime
  holds not n divides 1279 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
