
theorem
  3581 is prime
proof
  now
    3581 = 2*1790 + 1; hence not 2 divides 3581 by NAT_4:9;
    3581 = 3*1193 + 2; hence not 3 divides 3581 by NAT_4:9;
    3581 = 5*716 + 1; hence not 5 divides 3581 by NAT_4:9;
    3581 = 7*511 + 4; hence not 7 divides 3581 by NAT_4:9;
    3581 = 11*325 + 6; hence not 11 divides 3581 by NAT_4:9;
    3581 = 13*275 + 6; hence not 13 divides 3581 by NAT_4:9;
    3581 = 17*210 + 11; hence not 17 divides 3581 by NAT_4:9;
    3581 = 19*188 + 9; hence not 19 divides 3581 by NAT_4:9;
    3581 = 23*155 + 16; hence not 23 divides 3581 by NAT_4:9;
    3581 = 29*123 + 14; hence not 29 divides 3581 by NAT_4:9;
    3581 = 31*115 + 16; hence not 31 divides 3581 by NAT_4:9;
    3581 = 37*96 + 29; hence not 37 divides 3581 by NAT_4:9;
    3581 = 41*87 + 14; hence not 41 divides 3581 by NAT_4:9;
    3581 = 43*83 + 12; hence not 43 divides 3581 by NAT_4:9;
    3581 = 47*76 + 9; hence not 47 divides 3581 by NAT_4:9;
    3581 = 53*67 + 30; hence not 53 divides 3581 by NAT_4:9;
    3581 = 59*60 + 41; hence not 59 divides 3581 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3581 & n is prime
  holds not n divides 3581 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
