
theorem
  3593 is prime
proof
  now
    3593 = 2*1796 + 1; hence not 2 divides 3593 by NAT_4:9;
    3593 = 3*1197 + 2; hence not 3 divides 3593 by NAT_4:9;
    3593 = 5*718 + 3; hence not 5 divides 3593 by NAT_4:9;
    3593 = 7*513 + 2; hence not 7 divides 3593 by NAT_4:9;
    3593 = 11*326 + 7; hence not 11 divides 3593 by NAT_4:9;
    3593 = 13*276 + 5; hence not 13 divides 3593 by NAT_4:9;
    3593 = 17*211 + 6; hence not 17 divides 3593 by NAT_4:9;
    3593 = 19*189 + 2; hence not 19 divides 3593 by NAT_4:9;
    3593 = 23*156 + 5; hence not 23 divides 3593 by NAT_4:9;
    3593 = 29*123 + 26; hence not 29 divides 3593 by NAT_4:9;
    3593 = 31*115 + 28; hence not 31 divides 3593 by NAT_4:9;
    3593 = 37*97 + 4; hence not 37 divides 3593 by NAT_4:9;
    3593 = 41*87 + 26; hence not 41 divides 3593 by NAT_4:9;
    3593 = 43*83 + 24; hence not 43 divides 3593 by NAT_4:9;
    3593 = 47*76 + 21; hence not 47 divides 3593 by NAT_4:9;
    3593 = 53*67 + 42; hence not 53 divides 3593 by NAT_4:9;
    3593 = 59*60 + 53; hence not 59 divides 3593 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3593 & n is prime
  holds not n divides 3593 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
