
theorem
  5011 is prime
proof
  now
    5011 = 2*2505 + 1; hence not 2 divides 5011 by NAT_4:9;
    5011 = 3*1670 + 1; hence not 3 divides 5011 by NAT_4:9;
    5011 = 5*1002 + 1; hence not 5 divides 5011 by NAT_4:9;
    5011 = 7*715 + 6; hence not 7 divides 5011 by NAT_4:9;
    5011 = 11*455 + 6; hence not 11 divides 5011 by NAT_4:9;
    5011 = 13*385 + 6; hence not 13 divides 5011 by NAT_4:9;
    5011 = 17*294 + 13; hence not 17 divides 5011 by NAT_4:9;
    5011 = 19*263 + 14; hence not 19 divides 5011 by NAT_4:9;
    5011 = 23*217 + 20; hence not 23 divides 5011 by NAT_4:9;
    5011 = 29*172 + 23; hence not 29 divides 5011 by NAT_4:9;
    5011 = 31*161 + 20; hence not 31 divides 5011 by NAT_4:9;
    5011 = 37*135 + 16; hence not 37 divides 5011 by NAT_4:9;
    5011 = 41*122 + 9; hence not 41 divides 5011 by NAT_4:9;
    5011 = 43*116 + 23; hence not 43 divides 5011 by NAT_4:9;
    5011 = 47*106 + 29; hence not 47 divides 5011 by NAT_4:9;
    5011 = 53*94 + 29; hence not 53 divides 5011 by NAT_4:9;
    5011 = 59*84 + 55; hence not 59 divides 5011 by NAT_4:9;
    5011 = 61*82 + 9; hence not 61 divides 5011 by NAT_4:9;
    5011 = 67*74 + 53; hence not 67 divides 5011 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5011 & n is prime
  holds not n divides 5011 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
