
theorem
  3643 is prime
proof
  now
    3643 = 2*1821 + 1; hence not 2 divides 3643 by NAT_4:9;
    3643 = 3*1214 + 1; hence not 3 divides 3643 by NAT_4:9;
    3643 = 5*728 + 3; hence not 5 divides 3643 by NAT_4:9;
    3643 = 7*520 + 3; hence not 7 divides 3643 by NAT_4:9;
    3643 = 11*331 + 2; hence not 11 divides 3643 by NAT_4:9;
    3643 = 13*280 + 3; hence not 13 divides 3643 by NAT_4:9;
    3643 = 17*214 + 5; hence not 17 divides 3643 by NAT_4:9;
    3643 = 19*191 + 14; hence not 19 divides 3643 by NAT_4:9;
    3643 = 23*158 + 9; hence not 23 divides 3643 by NAT_4:9;
    3643 = 29*125 + 18; hence not 29 divides 3643 by NAT_4:9;
    3643 = 31*117 + 16; hence not 31 divides 3643 by NAT_4:9;
    3643 = 37*98 + 17; hence not 37 divides 3643 by NAT_4:9;
    3643 = 41*88 + 35; hence not 41 divides 3643 by NAT_4:9;
    3643 = 43*84 + 31; hence not 43 divides 3643 by NAT_4:9;
    3643 = 47*77 + 24; hence not 47 divides 3643 by NAT_4:9;
    3643 = 53*68 + 39; hence not 53 divides 3643 by NAT_4:9;
    3643 = 59*61 + 44; hence not 59 divides 3643 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3643 & n is prime
  holds not n divides 3643 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
