
theorem
  991 is prime
proof
  now
    991 = 2*495 + 1; hence not 2 divides 991 by NAT_4:9;
    991 = 3*330 + 1; hence not 3 divides 991 by NAT_4:9;
    991 = 5*198 + 1; hence not 5 divides 991 by NAT_4:9;
    991 = 7*141 + 4; hence not 7 divides 991 by NAT_4:9;
    991 = 11*90 + 1; hence not 11 divides 991 by NAT_4:9;
    991 = 13*76 + 3; hence not 13 divides 991 by NAT_4:9;
    991 = 17*58 + 5; hence not 17 divides 991 by NAT_4:9;
    991 = 19*52 + 3; hence not 19 divides 991 by NAT_4:9;
    991 = 23*43 + 2; hence not 23 divides 991 by NAT_4:9;
    991 = 29*34 + 5; hence not 29 divides 991 by NAT_4:9;
    991 = 31*31 + 30; hence not 31 divides 991 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 991 & n is prime
  holds not n divides 991 by XPRIMET1:22;
  hence thesis by NAT_4:14;
end;
