
theorem
  5023 is prime
proof
  now
    5023 = 2*2511 + 1; hence not 2 divides 5023 by NAT_4:9;
    5023 = 3*1674 + 1; hence not 3 divides 5023 by NAT_4:9;
    5023 = 5*1004 + 3; hence not 5 divides 5023 by NAT_4:9;
    5023 = 7*717 + 4; hence not 7 divides 5023 by NAT_4:9;
    5023 = 11*456 + 7; hence not 11 divides 5023 by NAT_4:9;
    5023 = 13*386 + 5; hence not 13 divides 5023 by NAT_4:9;
    5023 = 17*295 + 8; hence not 17 divides 5023 by NAT_4:9;
    5023 = 19*264 + 7; hence not 19 divides 5023 by NAT_4:9;
    5023 = 23*218 + 9; hence not 23 divides 5023 by NAT_4:9;
    5023 = 29*173 + 6; hence not 29 divides 5023 by NAT_4:9;
    5023 = 31*162 + 1; hence not 31 divides 5023 by NAT_4:9;
    5023 = 37*135 + 28; hence not 37 divides 5023 by NAT_4:9;
    5023 = 41*122 + 21; hence not 41 divides 5023 by NAT_4:9;
    5023 = 43*116 + 35; hence not 43 divides 5023 by NAT_4:9;
    5023 = 47*106 + 41; hence not 47 divides 5023 by NAT_4:9;
    5023 = 53*94 + 41; hence not 53 divides 5023 by NAT_4:9;
    5023 = 59*85 + 8; hence not 59 divides 5023 by NAT_4:9;
    5023 = 61*82 + 21; hence not 61 divides 5023 by NAT_4:9;
    5023 = 67*74 + 65; hence not 67 divides 5023 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5023 & n is prime
  holds not n divides 5023 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
