
theorem
  3083 is prime
proof
  now
    3083 = 2*1541 + 1; hence not 2 divides 3083 by NAT_4:9;
    3083 = 3*1027 + 2; hence not 3 divides 3083 by NAT_4:9;
    3083 = 5*616 + 3; hence not 5 divides 3083 by NAT_4:9;
    3083 = 7*440 + 3; hence not 7 divides 3083 by NAT_4:9;
    3083 = 11*280 + 3; hence not 11 divides 3083 by NAT_4:9;
    3083 = 13*237 + 2; hence not 13 divides 3083 by NAT_4:9;
    3083 = 17*181 + 6; hence not 17 divides 3083 by NAT_4:9;
    3083 = 19*162 + 5; hence not 19 divides 3083 by NAT_4:9;
    3083 = 23*134 + 1; hence not 23 divides 3083 by NAT_4:9;
    3083 = 29*106 + 9; hence not 29 divides 3083 by NAT_4:9;
    3083 = 31*99 + 14; hence not 31 divides 3083 by NAT_4:9;
    3083 = 37*83 + 12; hence not 37 divides 3083 by NAT_4:9;
    3083 = 41*75 + 8; hence not 41 divides 3083 by NAT_4:9;
    3083 = 43*71 + 30; hence not 43 divides 3083 by NAT_4:9;
    3083 = 47*65 + 28; hence not 47 divides 3083 by NAT_4:9;
    3083 = 53*58 + 9; hence not 53 divides 3083 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3083 & n is prime
  holds not n divides 3083 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
