
theorem
  5419 is prime
proof
  now
    5419 = 2*2709 + 1; hence not 2 divides 5419 by NAT_4:9;
    5419 = 3*1806 + 1; hence not 3 divides 5419 by NAT_4:9;
    5419 = 5*1083 + 4; hence not 5 divides 5419 by NAT_4:9;
    5419 = 7*774 + 1; hence not 7 divides 5419 by NAT_4:9;
    5419 = 11*492 + 7; hence not 11 divides 5419 by NAT_4:9;
    5419 = 13*416 + 11; hence not 13 divides 5419 by NAT_4:9;
    5419 = 17*318 + 13; hence not 17 divides 5419 by NAT_4:9;
    5419 = 19*285 + 4; hence not 19 divides 5419 by NAT_4:9;
    5419 = 23*235 + 14; hence not 23 divides 5419 by NAT_4:9;
    5419 = 29*186 + 25; hence not 29 divides 5419 by NAT_4:9;
    5419 = 31*174 + 25; hence not 31 divides 5419 by NAT_4:9;
    5419 = 37*146 + 17; hence not 37 divides 5419 by NAT_4:9;
    5419 = 41*132 + 7; hence not 41 divides 5419 by NAT_4:9;
    5419 = 43*126 + 1; hence not 43 divides 5419 by NAT_4:9;
    5419 = 47*115 + 14; hence not 47 divides 5419 by NAT_4:9;
    5419 = 53*102 + 13; hence not 53 divides 5419 by NAT_4:9;
    5419 = 59*91 + 50; hence not 59 divides 5419 by NAT_4:9;
    5419 = 61*88 + 51; hence not 61 divides 5419 by NAT_4:9;
    5419 = 67*80 + 59; hence not 67 divides 5419 by NAT_4:9;
    5419 = 71*76 + 23; hence not 71 divides 5419 by NAT_4:9;
    5419 = 73*74 + 17; hence not 73 divides 5419 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5419 & n is prime
  holds not n divides 5419 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
