
theorem
  3739 is prime
proof
  now
    3739 = 2*1869 + 1; hence not 2 divides 3739 by NAT_4:9;
    3739 = 3*1246 + 1; hence not 3 divides 3739 by NAT_4:9;
    3739 = 5*747 + 4; hence not 5 divides 3739 by NAT_4:9;
    3739 = 7*534 + 1; hence not 7 divides 3739 by NAT_4:9;
    3739 = 11*339 + 10; hence not 11 divides 3739 by NAT_4:9;
    3739 = 13*287 + 8; hence not 13 divides 3739 by NAT_4:9;
    3739 = 17*219 + 16; hence not 17 divides 3739 by NAT_4:9;
    3739 = 19*196 + 15; hence not 19 divides 3739 by NAT_4:9;
    3739 = 23*162 + 13; hence not 23 divides 3739 by NAT_4:9;
    3739 = 29*128 + 27; hence not 29 divides 3739 by NAT_4:9;
    3739 = 31*120 + 19; hence not 31 divides 3739 by NAT_4:9;
    3739 = 37*101 + 2; hence not 37 divides 3739 by NAT_4:9;
    3739 = 41*91 + 8; hence not 41 divides 3739 by NAT_4:9;
    3739 = 43*86 + 41; hence not 43 divides 3739 by NAT_4:9;
    3739 = 47*79 + 26; hence not 47 divides 3739 by NAT_4:9;
    3739 = 53*70 + 29; hence not 53 divides 3739 by NAT_4:9;
    3739 = 59*63 + 22; hence not 59 divides 3739 by NAT_4:9;
    3739 = 61*61 + 18; hence not 61 divides 3739 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3739 & n is prime
  holds not n divides 3739 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
