
theorem
  7109 is prime
proof
  now
    7109 = 2*3554 + 1; hence not 2 divides 7109 by NAT_4:9;
    7109 = 3*2369 + 2; hence not 3 divides 7109 by NAT_4:9;
    7109 = 5*1421 + 4; hence not 5 divides 7109 by NAT_4:9;
    7109 = 7*1015 + 4; hence not 7 divides 7109 by NAT_4:9;
    7109 = 11*646 + 3; hence not 11 divides 7109 by NAT_4:9;
    7109 = 13*546 + 11; hence not 13 divides 7109 by NAT_4:9;
    7109 = 17*418 + 3; hence not 17 divides 7109 by NAT_4:9;
    7109 = 19*374 + 3; hence not 19 divides 7109 by NAT_4:9;
    7109 = 23*309 + 2; hence not 23 divides 7109 by NAT_4:9;
    7109 = 29*245 + 4; hence not 29 divides 7109 by NAT_4:9;
    7109 = 31*229 + 10; hence not 31 divides 7109 by NAT_4:9;
    7109 = 37*192 + 5; hence not 37 divides 7109 by NAT_4:9;
    7109 = 41*173 + 16; hence not 41 divides 7109 by NAT_4:9;
    7109 = 43*165 + 14; hence not 43 divides 7109 by NAT_4:9;
    7109 = 47*151 + 12; hence not 47 divides 7109 by NAT_4:9;
    7109 = 53*134 + 7; hence not 53 divides 7109 by NAT_4:9;
    7109 = 59*120 + 29; hence not 59 divides 7109 by NAT_4:9;
    7109 = 61*116 + 33; hence not 61 divides 7109 by NAT_4:9;
    7109 = 67*106 + 7; hence not 67 divides 7109 by NAT_4:9;
    7109 = 71*100 + 9; hence not 71 divides 7109 by NAT_4:9;
    7109 = 73*97 + 28; hence not 73 divides 7109 by NAT_4:9;
    7109 = 79*89 + 78; hence not 79 divides 7109 by NAT_4:9;
    7109 = 83*85 + 54; hence not 83 divides 7109 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7109 & n is prime
  holds not n divides 7109 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
