
theorem
  7069 is prime
proof
  now
    7069 = 2*3534 + 1; hence not 2 divides 7069 by NAT_4:9;
    7069 = 3*2356 + 1; hence not 3 divides 7069 by NAT_4:9;
    7069 = 5*1413 + 4; hence not 5 divides 7069 by NAT_4:9;
    7069 = 7*1009 + 6; hence not 7 divides 7069 by NAT_4:9;
    7069 = 11*642 + 7; hence not 11 divides 7069 by NAT_4:9;
    7069 = 13*543 + 10; hence not 13 divides 7069 by NAT_4:9;
    7069 = 17*415 + 14; hence not 17 divides 7069 by NAT_4:9;
    7069 = 19*372 + 1; hence not 19 divides 7069 by NAT_4:9;
    7069 = 23*307 + 8; hence not 23 divides 7069 by NAT_4:9;
    7069 = 29*243 + 22; hence not 29 divides 7069 by NAT_4:9;
    7069 = 31*228 + 1; hence not 31 divides 7069 by NAT_4:9;
    7069 = 37*191 + 2; hence not 37 divides 7069 by NAT_4:9;
    7069 = 41*172 + 17; hence not 41 divides 7069 by NAT_4:9;
    7069 = 43*164 + 17; hence not 43 divides 7069 by NAT_4:9;
    7069 = 47*150 + 19; hence not 47 divides 7069 by NAT_4:9;
    7069 = 53*133 + 20; hence not 53 divides 7069 by NAT_4:9;
    7069 = 59*119 + 48; hence not 59 divides 7069 by NAT_4:9;
    7069 = 61*115 + 54; hence not 61 divides 7069 by NAT_4:9;
    7069 = 67*105 + 34; hence not 67 divides 7069 by NAT_4:9;
    7069 = 71*99 + 40; hence not 71 divides 7069 by NAT_4:9;
    7069 = 73*96 + 61; hence not 73 divides 7069 by NAT_4:9;
    7069 = 79*89 + 38; hence not 79 divides 7069 by NAT_4:9;
    7069 = 83*85 + 14; hence not 83 divides 7069 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7069 & n is prime
  holds not n divides 7069 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
