
theorem
  5519 is prime
proof
  now
    5519 = 2*2759 + 1; hence not 2 divides 5519 by NAT_4:9;
    5519 = 3*1839 + 2; hence not 3 divides 5519 by NAT_4:9;
    5519 = 5*1103 + 4; hence not 5 divides 5519 by NAT_4:9;
    5519 = 7*788 + 3; hence not 7 divides 5519 by NAT_4:9;
    5519 = 11*501 + 8; hence not 11 divides 5519 by NAT_4:9;
    5519 = 13*424 + 7; hence not 13 divides 5519 by NAT_4:9;
    5519 = 17*324 + 11; hence not 17 divides 5519 by NAT_4:9;
    5519 = 19*290 + 9; hence not 19 divides 5519 by NAT_4:9;
    5519 = 23*239 + 22; hence not 23 divides 5519 by NAT_4:9;
    5519 = 29*190 + 9; hence not 29 divides 5519 by NAT_4:9;
    5519 = 31*178 + 1; hence not 31 divides 5519 by NAT_4:9;
    5519 = 37*149 + 6; hence not 37 divides 5519 by NAT_4:9;
    5519 = 41*134 + 25; hence not 41 divides 5519 by NAT_4:9;
    5519 = 43*128 + 15; hence not 43 divides 5519 by NAT_4:9;
    5519 = 47*117 + 20; hence not 47 divides 5519 by NAT_4:9;
    5519 = 53*104 + 7; hence not 53 divides 5519 by NAT_4:9;
    5519 = 59*93 + 32; hence not 59 divides 5519 by NAT_4:9;
    5519 = 61*90 + 29; hence not 61 divides 5519 by NAT_4:9;
    5519 = 67*82 + 25; hence not 67 divides 5519 by NAT_4:9;
    5519 = 71*77 + 52; hence not 71 divides 5519 by NAT_4:9;
    5519 = 73*75 + 44; hence not 73 divides 5519 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5519 & n is prime
  holds not n divides 5519 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
