
theorem
  2579 is prime
proof
  now
    2579 = 2*1289 + 1; hence not 2 divides 2579 by NAT_4:9;
    2579 = 3*859 + 2; hence not 3 divides 2579 by NAT_4:9;
    2579 = 5*515 + 4; hence not 5 divides 2579 by NAT_4:9;
    2579 = 7*368 + 3; hence not 7 divides 2579 by NAT_4:9;
    2579 = 11*234 + 5; hence not 11 divides 2579 by NAT_4:9;
    2579 = 13*198 + 5; hence not 13 divides 2579 by NAT_4:9;
    2579 = 17*151 + 12; hence not 17 divides 2579 by NAT_4:9;
    2579 = 19*135 + 14; hence not 19 divides 2579 by NAT_4:9;
    2579 = 23*112 + 3; hence not 23 divides 2579 by NAT_4:9;
    2579 = 29*88 + 27; hence not 29 divides 2579 by NAT_4:9;
    2579 = 31*83 + 6; hence not 31 divides 2579 by NAT_4:9;
    2579 = 37*69 + 26; hence not 37 divides 2579 by NAT_4:9;
    2579 = 41*62 + 37; hence not 41 divides 2579 by NAT_4:9;
    2579 = 43*59 + 42; hence not 43 divides 2579 by NAT_4:9;
    2579 = 47*54 + 41; hence not 47 divides 2579 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2579 & n is prime
  holds not n divides 2579 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
