
theorem
  3769 is prime
proof
  now
    3769 = 2*1884 + 1; hence not 2 divides 3769 by NAT_4:9;
    3769 = 3*1256 + 1; hence not 3 divides 3769 by NAT_4:9;
    3769 = 5*753 + 4; hence not 5 divides 3769 by NAT_4:9;
    3769 = 7*538 + 3; hence not 7 divides 3769 by NAT_4:9;
    3769 = 11*342 + 7; hence not 11 divides 3769 by NAT_4:9;
    3769 = 13*289 + 12; hence not 13 divides 3769 by NAT_4:9;
    3769 = 17*221 + 12; hence not 17 divides 3769 by NAT_4:9;
    3769 = 19*198 + 7; hence not 19 divides 3769 by NAT_4:9;
    3769 = 23*163 + 20; hence not 23 divides 3769 by NAT_4:9;
    3769 = 29*129 + 28; hence not 29 divides 3769 by NAT_4:9;
    3769 = 31*121 + 18; hence not 31 divides 3769 by NAT_4:9;
    3769 = 37*101 + 32; hence not 37 divides 3769 by NAT_4:9;
    3769 = 41*91 + 38; hence not 41 divides 3769 by NAT_4:9;
    3769 = 43*87 + 28; hence not 43 divides 3769 by NAT_4:9;
    3769 = 47*80 + 9; hence not 47 divides 3769 by NAT_4:9;
    3769 = 53*71 + 6; hence not 53 divides 3769 by NAT_4:9;
    3769 = 59*63 + 52; hence not 59 divides 3769 by NAT_4:9;
    3769 = 61*61 + 48; hence not 61 divides 3769 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3769 & n is prime
  holds not n divides 3769 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
