
theorem
  1291 is prime
proof
  now
    1291 = 2*645 + 1; hence not 2 divides 1291 by NAT_4:9;
    1291 = 3*430 + 1; hence not 3 divides 1291 by NAT_4:9;
    1291 = 5*258 + 1; hence not 5 divides 1291 by NAT_4:9;
    1291 = 7*184 + 3; hence not 7 divides 1291 by NAT_4:9;
    1291 = 11*117 + 4; hence not 11 divides 1291 by NAT_4:9;
    1291 = 13*99 + 4; hence not 13 divides 1291 by NAT_4:9;
    1291 = 17*75 + 16; hence not 17 divides 1291 by NAT_4:9;
    1291 = 19*67 + 18; hence not 19 divides 1291 by NAT_4:9;
    1291 = 23*56 + 3; hence not 23 divides 1291 by NAT_4:9;
    1291 = 29*44 + 15; hence not 29 divides 1291 by NAT_4:9;
    1291 = 31*41 + 20; hence not 31 divides 1291 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 1291 & n is prime
  holds not n divides 1291 by XPRIMET1:22;
  hence thesis by NAT_4:14;
