
theorem
  3119 is prime
proof
  now
    3119 = 2*1559 + 1; hence not 2 divides 3119 by NAT_4:9;
    3119 = 3*1039 + 2; hence not 3 divides 3119 by NAT_4:9;
    3119 = 5*623 + 4; hence not 5 divides 3119 by NAT_4:9;
    3119 = 7*445 + 4; hence not 7 divides 3119 by NAT_4:9;
    3119 = 11*283 + 6; hence not 11 divides 3119 by NAT_4:9;
    3119 = 13*239 + 12; hence not 13 divides 3119 by NAT_4:9;
    3119 = 17*183 + 8; hence not 17 divides 3119 by NAT_4:9;
    3119 = 19*164 + 3; hence not 19 divides 3119 by NAT_4:9;
    3119 = 23*135 + 14; hence not 23 divides 3119 by NAT_4:9;
    3119 = 29*107 + 16; hence not 29 divides 3119 by NAT_4:9;
    3119 = 31*100 + 19; hence not 31 divides 3119 by NAT_4:9;
    3119 = 37*84 + 11; hence not 37 divides 3119 by NAT_4:9;
    3119 = 41*76 + 3; hence not 41 divides 3119 by NAT_4:9;
    3119 = 43*72 + 23; hence not 43 divides 3119 by NAT_4:9;
    3119 = 47*66 + 17; hence not 47 divides 3119 by NAT_4:9;
    3119 = 53*58 + 45; hence not 53 divides 3119 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3119 & n is prime
  holds not n divides 3119 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
