
theorem
  3631 is prime
proof
  now
    3631 = 2*1815 + 1; hence not 2 divides 3631 by NAT_4:9;
    3631 = 3*1210 + 1; hence not 3 divides 3631 by NAT_4:9;
    3631 = 5*726 + 1; hence not 5 divides 3631 by NAT_4:9;
    3631 = 7*518 + 5; hence not 7 divides 3631 by NAT_4:9;
    3631 = 11*330 + 1; hence not 11 divides 3631 by NAT_4:9;
    3631 = 13*279 + 4; hence not 13 divides 3631 by NAT_4:9;
    3631 = 17*213 + 10; hence not 17 divides 3631 by NAT_4:9;
    3631 = 19*191 + 2; hence not 19 divides 3631 by NAT_4:9;
    3631 = 23*157 + 20; hence not 23 divides 3631 by NAT_4:9;
    3631 = 29*125 + 6; hence not 29 divides 3631 by NAT_4:9;
    3631 = 31*117 + 4; hence not 31 divides 3631 by NAT_4:9;
    3631 = 37*98 + 5; hence not 37 divides 3631 by NAT_4:9;
    3631 = 41*88 + 23; hence not 41 divides 3631 by NAT_4:9;
    3631 = 43*84 + 19; hence not 43 divides 3631 by NAT_4:9;
    3631 = 47*77 + 12; hence not 47 divides 3631 by NAT_4:9;
    3631 = 53*68 + 27; hence not 53 divides 3631 by NAT_4:9;
    3631 = 59*61 + 32; hence not 59 divides 3631 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3631 & n is prime
  holds not n divides 3631 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
