
theorem
  3023 is prime
proof
  now
    3023 = 2*1511 + 1; hence not 2 divides 3023 by NAT_4:9;
    3023 = 3*1007 + 2; hence not 3 divides 3023 by NAT_4:9;
    3023 = 5*604 + 3; hence not 5 divides 3023 by NAT_4:9;
    3023 = 7*431 + 6; hence not 7 divides 3023 by NAT_4:9;
    3023 = 11*274 + 9; hence not 11 divides 3023 by NAT_4:9;
    3023 = 13*232 + 7; hence not 13 divides 3023 by NAT_4:9;
    3023 = 17*177 + 14; hence not 17 divides 3023 by NAT_4:9;
    3023 = 19*159 + 2; hence not 19 divides 3023 by NAT_4:9;
    3023 = 23*131 + 10; hence not 23 divides 3023 by NAT_4:9;
    3023 = 29*104 + 7; hence not 29 divides 3023 by NAT_4:9;
    3023 = 31*97 + 16; hence not 31 divides 3023 by NAT_4:9;
    3023 = 37*81 + 26; hence not 37 divides 3023 by NAT_4:9;
    3023 = 41*73 + 30; hence not 41 divides 3023 by NAT_4:9;
    3023 = 43*70 + 13; hence not 43 divides 3023 by NAT_4:9;
    3023 = 47*64 + 15; hence not 47 divides 3023 by NAT_4:9;
    3023 = 53*57 + 2; hence not 53 divides 3023 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3023 & n is prime
  holds not n divides 3023 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
