
theorem
  541 is prime
proof
  now
    541 = 2*270 + 1; hence not 2 divides 541 by NAT_4:9;
    541 = 3*180 + 1; hence not 3 divides 541 by NAT_4:9;
    541 = 5*108 + 1; hence not 5 divides 541 by NAT_4:9;
    541 = 7*77 + 2; hence not 7 divides 541 by NAT_4:9;
    541 = 11*49 + 2; hence not 11 divides 541 by NAT_4:9;
    541 = 13*41 + 8; hence not 13 divides 541 by NAT_4:9;
    541 = 17*31 + 14; hence not 17 divides 541 by NAT_4:9;
    541 = 19*28 + 9; hence not 19 divides 541 by NAT_4:9;
    541 = 23*23 + 12; hence not 23 divides 541 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 541 & n is prime
  holds not n divides 541 by XPRIMET1:18;
  hence thesis by NAT_4:14;
