
theorem
  5119 is prime
proof
  now
    5119 = 2*2559 + 1; hence not 2 divides 5119 by NAT_4:9;
    5119 = 3*1706 + 1; hence not 3 divides 5119 by NAT_4:9;
    5119 = 5*1023 + 4; hence not 5 divides 5119 by NAT_4:9;
    5119 = 7*731 + 2; hence not 7 divides 5119 by NAT_4:9;
    5119 = 11*465 + 4; hence not 11 divides 5119 by NAT_4:9;
    5119 = 13*393 + 10; hence not 13 divides 5119 by NAT_4:9;
    5119 = 17*301 + 2; hence not 17 divides 5119 by NAT_4:9;
    5119 = 19*269 + 8; hence not 19 divides 5119 by NAT_4:9;
    5119 = 23*222 + 13; hence not 23 divides 5119 by NAT_4:9;
    5119 = 29*176 + 15; hence not 29 divides 5119 by NAT_4:9;
    5119 = 31*165 + 4; hence not 31 divides 5119 by NAT_4:9;
    5119 = 37*138 + 13; hence not 37 divides 5119 by NAT_4:9;
    5119 = 41*124 + 35; hence not 41 divides 5119 by NAT_4:9;
    5119 = 43*119 + 2; hence not 43 divides 5119 by NAT_4:9;
    5119 = 47*108 + 43; hence not 47 divides 5119 by NAT_4:9;
    5119 = 53*96 + 31; hence not 53 divides 5119 by NAT_4:9;
    5119 = 59*86 + 45; hence not 59 divides 5119 by NAT_4:9;
    5119 = 61*83 + 56; hence not 61 divides 5119 by NAT_4:9;
    5119 = 67*76 + 27; hence not 67 divides 5119 by NAT_4:9;
    5119 = 71*72 + 7; hence not 71 divides 5119 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5119 & n is prime
  holds not n divides 5119 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
