
theorem
  7043 is prime
proof
  now
    7043 = 2*3521 + 1; hence not 2 divides 7043 by NAT_4:9;
    7043 = 3*2347 + 2; hence not 3 divides 7043 by NAT_4:9;
    7043 = 5*1408 + 3; hence not 5 divides 7043 by NAT_4:9;
    7043 = 7*1006 + 1; hence not 7 divides 7043 by NAT_4:9;
    7043 = 11*640 + 3; hence not 11 divides 7043 by NAT_4:9;
    7043 = 13*541 + 10; hence not 13 divides 7043 by NAT_4:9;
    7043 = 17*414 + 5; hence not 17 divides 7043 by NAT_4:9;
    7043 = 19*370 + 13; hence not 19 divides 7043 by NAT_4:9;
    7043 = 23*306 + 5; hence not 23 divides 7043 by NAT_4:9;
    7043 = 29*242 + 25; hence not 29 divides 7043 by NAT_4:9;
    7043 = 31*227 + 6; hence not 31 divides 7043 by NAT_4:9;
    7043 = 37*190 + 13; hence not 37 divides 7043 by NAT_4:9;
    7043 = 41*171 + 32; hence not 41 divides 7043 by NAT_4:9;
    7043 = 43*163 + 34; hence not 43 divides 7043 by NAT_4:9;
    7043 = 47*149 + 40; hence not 47 divides 7043 by NAT_4:9;
    7043 = 53*132 + 47; hence not 53 divides 7043 by NAT_4:9;
    7043 = 59*119 + 22; hence not 59 divides 7043 by NAT_4:9;
    7043 = 61*115 + 28; hence not 61 divides 7043 by NAT_4:9;
    7043 = 67*105 + 8; hence not 67 divides 7043 by NAT_4:9;
    7043 = 71*99 + 14; hence not 71 divides 7043 by NAT_4:9;
    7043 = 73*96 + 35; hence not 73 divides 7043 by NAT_4:9;
    7043 = 79*89 + 12; hence not 79 divides 7043 by NAT_4:9;
    7043 = 83*84 + 71; hence not 83 divides 7043 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7043 & n is prime
  holds not n divides 7043 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
