
theorem
  6143 is prime
proof
  now
    6143 = 2*3071 + 1; hence not 2 divides 6143 by NAT_4:9;
    6143 = 3*2047 + 2; hence not 3 divides 6143 by NAT_4:9;
    6143 = 5*1228 + 3; hence not 5 divides 6143 by NAT_4:9;
    6143 = 7*877 + 4; hence not 7 divides 6143 by NAT_4:9;
    6143 = 11*558 + 5; hence not 11 divides 6143 by NAT_4:9;
    6143 = 13*472 + 7; hence not 13 divides 6143 by NAT_4:9;
    6143 = 17*361 + 6; hence not 17 divides 6143 by NAT_4:9;
    6143 = 19*323 + 6; hence not 19 divides 6143 by NAT_4:9;
    6143 = 23*267 + 2; hence not 23 divides 6143 by NAT_4:9;
    6143 = 29*211 + 24; hence not 29 divides 6143 by NAT_4:9;
    6143 = 31*198 + 5; hence not 31 divides 6143 by NAT_4:9;
    6143 = 37*166 + 1; hence not 37 divides 6143 by NAT_4:9;
    6143 = 41*149 + 34; hence not 41 divides 6143 by NAT_4:9;
    6143 = 43*142 + 37; hence not 43 divides 6143 by NAT_4:9;
    6143 = 47*130 + 33; hence not 47 divides 6143 by NAT_4:9;
    6143 = 53*115 + 48; hence not 53 divides 6143 by NAT_4:9;
    6143 = 59*104 + 7; hence not 59 divides 6143 by NAT_4:9;
    6143 = 61*100 + 43; hence not 61 divides 6143 by NAT_4:9;
    6143 = 67*91 + 46; hence not 67 divides 6143 by NAT_4:9;
    6143 = 71*86 + 37; hence not 71 divides 6143 by NAT_4:9;
    6143 = 73*84 + 11; hence not 73 divides 6143 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6143 & n is prime
  holds not n divides 6143 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
