
theorem
  3727 is prime
proof
  now
    3727 = 2*1863 + 1; hence not 2 divides 3727 by NAT_4:9;
    3727 = 3*1242 + 1; hence not 3 divides 3727 by NAT_4:9;
    3727 = 5*745 + 2; hence not 5 divides 3727 by NAT_4:9;
    3727 = 7*532 + 3; hence not 7 divides 3727 by NAT_4:9;
    3727 = 11*338 + 9; hence not 11 divides 3727 by NAT_4:9;
    3727 = 13*286 + 9; hence not 13 divides 3727 by NAT_4:9;
    3727 = 17*219 + 4; hence not 17 divides 3727 by NAT_4:9;
    3727 = 19*196 + 3; hence not 19 divides 3727 by NAT_4:9;
    3727 = 23*162 + 1; hence not 23 divides 3727 by NAT_4:9;
    3727 = 29*128 + 15; hence not 29 divides 3727 by NAT_4:9;
    3727 = 31*120 + 7; hence not 31 divides 3727 by NAT_4:9;
    3727 = 37*100 + 27; hence not 37 divides 3727 by NAT_4:9;
    3727 = 41*90 + 37; hence not 41 divides 3727 by NAT_4:9;
    3727 = 43*86 + 29; hence not 43 divides 3727 by NAT_4:9;
    3727 = 47*79 + 14; hence not 47 divides 3727 by NAT_4:9;
    3727 = 53*70 + 17; hence not 53 divides 3727 by NAT_4:9;
    3727 = 59*63 + 10; hence not 59 divides 3727 by NAT_4:9;
    3727 = 61*61 + 6; hence not 61 divides 3727 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3727 & n is prime
  holds not n divides 3727 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
