
theorem
  5107 is prime
proof
  now
    5107 = 2*2553 + 1; hence not 2 divides 5107 by NAT_4:9;
    5107 = 3*1702 + 1; hence not 3 divides 5107 by NAT_4:9;
    5107 = 5*1021 + 2; hence not 5 divides 5107 by NAT_4:9;
    5107 = 7*729 + 4; hence not 7 divides 5107 by NAT_4:9;
    5107 = 11*464 + 3; hence not 11 divides 5107 by NAT_4:9;
    5107 = 13*392 + 11; hence not 13 divides 5107 by NAT_4:9;
    5107 = 17*300 + 7; hence not 17 divides 5107 by NAT_4:9;
    5107 = 19*268 + 15; hence not 19 divides 5107 by NAT_4:9;
    5107 = 23*222 + 1; hence not 23 divides 5107 by NAT_4:9;
    5107 = 29*176 + 3; hence not 29 divides 5107 by NAT_4:9;
    5107 = 31*164 + 23; hence not 31 divides 5107 by NAT_4:9;
    5107 = 37*138 + 1; hence not 37 divides 5107 by NAT_4:9;
    5107 = 41*124 + 23; hence not 41 divides 5107 by NAT_4:9;
    5107 = 43*118 + 33; hence not 43 divides 5107 by NAT_4:9;
    5107 = 47*108 + 31; hence not 47 divides 5107 by NAT_4:9;
    5107 = 53*96 + 19; hence not 53 divides 5107 by NAT_4:9;
    5107 = 59*86 + 33; hence not 59 divides 5107 by NAT_4:9;
    5107 = 61*83 + 44; hence not 61 divides 5107 by NAT_4:9;
    5107 = 67*76 + 15; hence not 67 divides 5107 by NAT_4:9;
    5107 = 71*71 + 66; hence not 71 divides 5107 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5107 & n is prime
  holds not n divides 5107 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
