
theorem
  6163 is prime
proof
  now
    6163 = 2*3081 + 1; hence not 2 divides 6163 by NAT_4:9;
    6163 = 3*2054 + 1; hence not 3 divides 6163 by NAT_4:9;
    6163 = 5*1232 + 3; hence not 5 divides 6163 by NAT_4:9;
    6163 = 7*880 + 3; hence not 7 divides 6163 by NAT_4:9;
    6163 = 11*560 + 3; hence not 11 divides 6163 by NAT_4:9;
    6163 = 13*474 + 1; hence not 13 divides 6163 by NAT_4:9;
    6163 = 17*362 + 9; hence not 17 divides 6163 by NAT_4:9;
    6163 = 19*324 + 7; hence not 19 divides 6163 by NAT_4:9;
    6163 = 23*267 + 22; hence not 23 divides 6163 by NAT_4:9;
    6163 = 29*212 + 15; hence not 29 divides 6163 by NAT_4:9;
    6163 = 31*198 + 25; hence not 31 divides 6163 by NAT_4:9;
    6163 = 37*166 + 21; hence not 37 divides 6163 by NAT_4:9;
    6163 = 41*150 + 13; hence not 41 divides 6163 by NAT_4:9;
    6163 = 43*143 + 14; hence not 43 divides 6163 by NAT_4:9;
    6163 = 47*131 + 6; hence not 47 divides 6163 by NAT_4:9;
    6163 = 53*116 + 15; hence not 53 divides 6163 by NAT_4:9;
    6163 = 59*104 + 27; hence not 59 divides 6163 by NAT_4:9;
    6163 = 61*101 + 2; hence not 61 divides 6163 by NAT_4:9;
    6163 = 67*91 + 66; hence not 67 divides 6163 by NAT_4:9;
    6163 = 71*86 + 57; hence not 71 divides 6163 by NAT_4:9;
    6163 = 73*84 + 31; hence not 73 divides 6163 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6163 & n is prime
  holds not n divides 6163 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
