
theorem
  1277 is prime
proof
  now
    1277 = 2*638 + 1; hence not 2 divides 1277 by NAT_4:9;
    1277 = 3*425 + 2; hence not 3 divides 1277 by NAT_4:9;
    1277 = 5*255 + 2; hence not 5 divides 1277 by NAT_4:9;
    1277 = 7*182 + 3; hence not 7 divides 1277 by NAT_4:9;
    1277 = 11*116 + 1; hence not 11 divides 1277 by NAT_4:9;
    1277 = 13*98 + 3; hence not 13 divides 1277 by NAT_4:9;
    1277 = 17*75 + 2; hence not 17 divides 1277 by NAT_4:9;
    1277 = 19*67 + 4; hence not 19 divides 1277 by NAT_4:9;
    1277 = 23*55 + 12; hence not 23 divides 1277 by NAT_4:9;
    1277 = 29*44 + 1; hence not 29 divides 1277 by NAT_4:9;
    1277 = 31*41 + 6; hence not 31 divides 1277 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1277 & n is prime
  holds not n divides 1277 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
