
theorem
  3677 is prime
proof
  now
    3677 = 2*1838 + 1; hence not 2 divides 3677 by NAT_4:9;
    3677 = 3*1225 + 2; hence not 3 divides 3677 by NAT_4:9;
    3677 = 5*735 + 2; hence not 5 divides 3677 by NAT_4:9;
    3677 = 7*525 + 2; hence not 7 divides 3677 by NAT_4:9;
    3677 = 11*334 + 3; hence not 11 divides 3677 by NAT_4:9;
    3677 = 13*282 + 11; hence not 13 divides 3677 by NAT_4:9;
    3677 = 17*216 + 5; hence not 17 divides 3677 by NAT_4:9;
    3677 = 19*193 + 10; hence not 19 divides 3677 by NAT_4:9;
    3677 = 23*159 + 20; hence not 23 divides 3677 by NAT_4:9;
    3677 = 29*126 + 23; hence not 29 divides 3677 by NAT_4:9;
    3677 = 31*118 + 19; hence not 31 divides 3677 by NAT_4:9;
    3677 = 37*99 + 14; hence not 37 divides 3677 by NAT_4:9;
    3677 = 41*89 + 28; hence not 41 divides 3677 by NAT_4:9;
    3677 = 43*85 + 22; hence not 43 divides 3677 by NAT_4:9;
    3677 = 47*78 + 11; hence not 47 divides 3677 by NAT_4:9;
    3677 = 53*69 + 20; hence not 53 divides 3677 by NAT_4:9;
    3677 = 59*62 + 19; hence not 59 divides 3677 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3677 & n is prime
  holds not n divides 3677 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
