
theorem
  5381 is prime
proof
  now
    5381 = 2*2690 + 1; hence not 2 divides 5381 by NAT_4:9;
    5381 = 3*1793 + 2; hence not 3 divides 5381 by NAT_4:9;
    5381 = 5*1076 + 1; hence not 5 divides 5381 by NAT_4:9;
    5381 = 7*768 + 5; hence not 7 divides 5381 by NAT_4:9;
    5381 = 11*489 + 2; hence not 11 divides 5381 by NAT_4:9;
    5381 = 13*413 + 12; hence not 13 divides 5381 by NAT_4:9;
    5381 = 17*316 + 9; hence not 17 divides 5381 by NAT_4:9;
    5381 = 19*283 + 4; hence not 19 divides 5381 by NAT_4:9;
    5381 = 23*233 + 22; hence not 23 divides 5381 by NAT_4:9;
    5381 = 29*185 + 16; hence not 29 divides 5381 by NAT_4:9;
    5381 = 31*173 + 18; hence not 31 divides 5381 by NAT_4:9;
    5381 = 37*145 + 16; hence not 37 divides 5381 by NAT_4:9;
    5381 = 41*131 + 10; hence not 41 divides 5381 by NAT_4:9;
    5381 = 43*125 + 6; hence not 43 divides 5381 by NAT_4:9;
    5381 = 47*114 + 23; hence not 47 divides 5381 by NAT_4:9;
    5381 = 53*101 + 28; hence not 53 divides 5381 by NAT_4:9;
    5381 = 59*91 + 12; hence not 59 divides 5381 by NAT_4:9;
    5381 = 61*88 + 13; hence not 61 divides 5381 by NAT_4:9;
    5381 = 67*80 + 21; hence not 67 divides 5381 by NAT_4:9;
    5381 = 71*75 + 56; hence not 71 divides 5381 by NAT_4:9;
    5381 = 73*73 + 52; hence not 73 divides 5381 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5381 & n is prime
  holds not n divides 5381 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
