
theorem
  5387 is prime
proof
  now
    5387 = 2*2693 + 1; hence not 2 divides 5387 by NAT_4:9;
    5387 = 3*1795 + 2; hence not 3 divides 5387 by NAT_4:9;
    5387 = 5*1077 + 2; hence not 5 divides 5387 by NAT_4:9;
    5387 = 7*769 + 4; hence not 7 divides 5387 by NAT_4:9;
    5387 = 11*489 + 8; hence not 11 divides 5387 by NAT_4:9;
    5387 = 13*414 + 5; hence not 13 divides 5387 by NAT_4:9;
    5387 = 17*316 + 15; hence not 17 divides 5387 by NAT_4:9;
    5387 = 19*283 + 10; hence not 19 divides 5387 by NAT_4:9;
    5387 = 23*234 + 5; hence not 23 divides 5387 by NAT_4:9;
    5387 = 29*185 + 22; hence not 29 divides 5387 by NAT_4:9;
    5387 = 31*173 + 24; hence not 31 divides 5387 by NAT_4:9;
    5387 = 37*145 + 22; hence not 37 divides 5387 by NAT_4:9;
    5387 = 41*131 + 16; hence not 41 divides 5387 by NAT_4:9;
    5387 = 43*125 + 12; hence not 43 divides 5387 by NAT_4:9;
    5387 = 47*114 + 29; hence not 47 divides 5387 by NAT_4:9;
    5387 = 53*101 + 34; hence not 53 divides 5387 by NAT_4:9;
    5387 = 59*91 + 18; hence not 59 divides 5387 by NAT_4:9;
    5387 = 61*88 + 19; hence not 61 divides 5387 by NAT_4:9;
    5387 = 67*80 + 27; hence not 67 divides 5387 by NAT_4:9;
    5387 = 71*75 + 62; hence not 71 divides 5387 by NAT_4:9;
    5387 = 73*73 + 58; hence not 73 divides 5387 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5387 & n is prime
  holds not n divides 5387 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
