
theorem
  7039 is prime
proof
  now
    7039 = 2*3519 + 1; hence not 2 divides 7039 by NAT_4:9;
    7039 = 3*2346 + 1; hence not 3 divides 7039 by NAT_4:9;
    7039 = 5*1407 + 4; hence not 5 divides 7039 by NAT_4:9;
    7039 = 7*1005 + 4; hence not 7 divides 7039 by NAT_4:9;
    7039 = 11*639 + 10; hence not 11 divides 7039 by NAT_4:9;
    7039 = 13*541 + 6; hence not 13 divides 7039 by NAT_4:9;
    7039 = 17*414 + 1; hence not 17 divides 7039 by NAT_4:9;
    7039 = 19*370 + 9; hence not 19 divides 7039 by NAT_4:9;
    7039 = 23*306 + 1; hence not 23 divides 7039 by NAT_4:9;
    7039 = 29*242 + 21; hence not 29 divides 7039 by NAT_4:9;
    7039 = 31*227 + 2; hence not 31 divides 7039 by NAT_4:9;
    7039 = 37*190 + 9; hence not 37 divides 7039 by NAT_4:9;
    7039 = 41*171 + 28; hence not 41 divides 7039 by NAT_4:9;
    7039 = 43*163 + 30; hence not 43 divides 7039 by NAT_4:9;
    7039 = 47*149 + 36; hence not 47 divides 7039 by NAT_4:9;
    7039 = 53*132 + 43; hence not 53 divides 7039 by NAT_4:9;
    7039 = 59*119 + 18; hence not 59 divides 7039 by NAT_4:9;
    7039 = 61*115 + 24; hence not 61 divides 7039 by NAT_4:9;
    7039 = 67*105 + 4; hence not 67 divides 7039 by NAT_4:9;
    7039 = 71*99 + 10; hence not 71 divides 7039 by NAT_4:9;
    7039 = 73*96 + 31; hence not 73 divides 7039 by NAT_4:9;
    7039 = 79*89 + 8; hence not 79 divides 7039 by NAT_4:9;
    7039 = 83*84 + 67; hence not 83 divides 7039 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7039 & n is prime
  holds not n divides 7039 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
