
theorem
  3719 is prime
proof
  now
    3719 = 2*1859 + 1; hence not 2 divides 3719 by NAT_4:9;
    3719 = 3*1239 + 2; hence not 3 divides 3719 by NAT_4:9;
    3719 = 5*743 + 4; hence not 5 divides 3719 by NAT_4:9;
    3719 = 7*531 + 2; hence not 7 divides 3719 by NAT_4:9;
    3719 = 11*338 + 1; hence not 11 divides 3719 by NAT_4:9;
    3719 = 13*286 + 1; hence not 13 divides 3719 by NAT_4:9;
    3719 = 17*218 + 13; hence not 17 divides 3719 by NAT_4:9;
    3719 = 19*195 + 14; hence not 19 divides 3719 by NAT_4:9;
    3719 = 23*161 + 16; hence not 23 divides 3719 by NAT_4:9;
    3719 = 29*128 + 7; hence not 29 divides 3719 by NAT_4:9;
    3719 = 31*119 + 30; hence not 31 divides 3719 by NAT_4:9;
    3719 = 37*100 + 19; hence not 37 divides 3719 by NAT_4:9;
    3719 = 41*90 + 29; hence not 41 divides 3719 by NAT_4:9;
    3719 = 43*86 + 21; hence not 43 divides 3719 by NAT_4:9;
    3719 = 47*79 + 6; hence not 47 divides 3719 by NAT_4:9;
    3719 = 53*70 + 9; hence not 53 divides 3719 by NAT_4:9;
    3719 = 59*63 + 2; hence not 59 divides 3719 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3719 & n is prime
  holds not n divides 3719 by XPRIMET1:34;
  hence thesis by NAT_4:14;
end;
