
theorem
  5059 is prime
proof
  now
    5059 = 2*2529 + 1; hence not 2 divides 5059 by NAT_4:9;
    5059 = 3*1686 + 1; hence not 3 divides 5059 by NAT_4:9;
    5059 = 5*1011 + 4; hence not 5 divides 5059 by NAT_4:9;
    5059 = 7*722 + 5; hence not 7 divides 5059 by NAT_4:9;
    5059 = 11*459 + 10; hence not 11 divides 5059 by NAT_4:9;
    5059 = 13*389 + 2; hence not 13 divides 5059 by NAT_4:9;
    5059 = 17*297 + 10; hence not 17 divides 5059 by NAT_4:9;
    5059 = 19*266 + 5; hence not 19 divides 5059 by NAT_4:9;
    5059 = 23*219 + 22; hence not 23 divides 5059 by NAT_4:9;
    5059 = 29*174 + 13; hence not 29 divides 5059 by NAT_4:9;
    5059 = 31*163 + 6; hence not 31 divides 5059 by NAT_4:9;
    5059 = 37*136 + 27; hence not 37 divides 5059 by NAT_4:9;
    5059 = 41*123 + 16; hence not 41 divides 5059 by NAT_4:9;
    5059 = 43*117 + 28; hence not 43 divides 5059 by NAT_4:9;
    5059 = 47*107 + 30; hence not 47 divides 5059 by NAT_4:9;
    5059 = 53*95 + 24; hence not 53 divides 5059 by NAT_4:9;
    5059 = 59*85 + 44; hence not 59 divides 5059 by NAT_4:9;
    5059 = 61*82 + 57; hence not 61 divides 5059 by NAT_4:9;
    5059 = 67*75 + 34; hence not 67 divides 5059 by NAT_4:9;
    5059 = 71*71 + 18; hence not 71 divides 5059 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5059 & n is prime
  holds not n divides 5059 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
