
theorem
  3079 is prime
proof
  now
    3079 = 2*1539 + 1; hence not 2 divides 3079 by NAT_4:9;
    3079 = 3*1026 + 1; hence not 3 divides 3079 by NAT_4:9;
    3079 = 5*615 + 4; hence not 5 divides 3079 by NAT_4:9;
    3079 = 7*439 + 6; hence not 7 divides 3079 by NAT_4:9;
    3079 = 11*279 + 10; hence not 11 divides 3079 by NAT_4:9;
    3079 = 13*236 + 11; hence not 13 divides 3079 by NAT_4:9;
    3079 = 17*181 + 2; hence not 17 divides 3079 by NAT_4:9;
    3079 = 19*162 + 1; hence not 19 divides 3079 by NAT_4:9;
    3079 = 23*133 + 20; hence not 23 divides 3079 by NAT_4:9;
    3079 = 29*106 + 5; hence not 29 divides 3079 by NAT_4:9;
    3079 = 31*99 + 10; hence not 31 divides 3079 by NAT_4:9;
    3079 = 37*83 + 8; hence not 37 divides 3079 by NAT_4:9;
    3079 = 41*75 + 4; hence not 41 divides 3079 by NAT_4:9;
    3079 = 43*71 + 26; hence not 43 divides 3079 by NAT_4:9;
    3079 = 47*65 + 24; hence not 47 divides 3079 by NAT_4:9;
    3079 = 53*58 + 5; hence not 53 divides 3079 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3079 & n is prime
  holds not n divides 3079 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
