
theorem
  3779 is prime
proof
  now
    3779 = 2*1889 + 1; hence not 2 divides 3779 by NAT_4:9;
    3779 = 3*1259 + 2; hence not 3 divides 3779 by NAT_4:9;
    3779 = 5*755 + 4; hence not 5 divides 3779 by NAT_4:9;
    3779 = 7*539 + 6; hence not 7 divides 3779 by NAT_4:9;
    3779 = 11*343 + 6; hence not 11 divides 3779 by NAT_4:9;
    3779 = 13*290 + 9; hence not 13 divides 3779 by NAT_4:9;
    3779 = 17*222 + 5; hence not 17 divides 3779 by NAT_4:9;
    3779 = 19*198 + 17; hence not 19 divides 3779 by NAT_4:9;
    3779 = 23*164 + 7; hence not 23 divides 3779 by NAT_4:9;
    3779 = 29*130 + 9; hence not 29 divides 3779 by NAT_4:9;
    3779 = 31*121 + 28; hence not 31 divides 3779 by NAT_4:9;
    3779 = 37*102 + 5; hence not 37 divides 3779 by NAT_4:9;
    3779 = 41*92 + 7; hence not 41 divides 3779 by NAT_4:9;
    3779 = 43*87 + 38; hence not 43 divides 3779 by NAT_4:9;
    3779 = 47*80 + 19; hence not 47 divides 3779 by NAT_4:9;
    3779 = 53*71 + 16; hence not 53 divides 3779 by NAT_4:9;
    3779 = 59*64 + 3; hence not 59 divides 3779 by NAT_4:9;
    3779 = 61*61 + 58; hence not 61 divides 3779 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3779 & n is prime
  holds not n divides 3779 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
