
theorem
  4133 is prime
proof
  now
    4133 = 2*2066 + 1; hence not 2 divides 4133 by NAT_4:9;
    4133 = 3*1377 + 2; hence not 3 divides 4133 by NAT_4:9;
    4133 = 5*826 + 3; hence not 5 divides 4133 by NAT_4:9;
    4133 = 7*590 + 3; hence not 7 divides 4133 by NAT_4:9;
    4133 = 11*375 + 8; hence not 11 divides 4133 by NAT_4:9;
    4133 = 13*317 + 12; hence not 13 divides 4133 by NAT_4:9;
    4133 = 17*243 + 2; hence not 17 divides 4133 by NAT_4:9;
    4133 = 19*217 + 10; hence not 19 divides 4133 by NAT_4:9;
    4133 = 23*179 + 16; hence not 23 divides 4133 by NAT_4:9;
    4133 = 29*142 + 15; hence not 29 divides 4133 by NAT_4:9;
    4133 = 31*133 + 10; hence not 31 divides 4133 by NAT_4:9;
    4133 = 37*111 + 26; hence not 37 divides 4133 by NAT_4:9;
    4133 = 41*100 + 33; hence not 41 divides 4133 by NAT_4:9;
    4133 = 43*96 + 5; hence not 43 divides 4133 by NAT_4:9;
    4133 = 47*87 + 44; hence not 47 divides 4133 by NAT_4:9;
    4133 = 53*77 + 52; hence not 53 divides 4133 by NAT_4:9;
    4133 = 59*70 + 3; hence not 59 divides 4133 by NAT_4:9;
    4133 = 61*67 + 46; hence not 61 divides 4133 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4133 & n is prime
  holds not n divides 4133 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
