
theorem
  3259 is prime
proof
  now
    3259 = 2*1629 + 1; hence not 2 divides 3259 by NAT_4:9;
    3259 = 3*1086 + 1; hence not 3 divides 3259 by NAT_4:9;
    3259 = 5*651 + 4; hence not 5 divides 3259 by NAT_4:9;
    3259 = 7*465 + 4; hence not 7 divides 3259 by NAT_4:9;
    3259 = 11*296 + 3; hence not 11 divides 3259 by NAT_4:9;
    3259 = 13*250 + 9; hence not 13 divides 3259 by NAT_4:9;
    3259 = 17*191 + 12; hence not 17 divides 3259 by NAT_4:9;
    3259 = 19*171 + 10; hence not 19 divides 3259 by NAT_4:9;
    3259 = 23*141 + 16; hence not 23 divides 3259 by NAT_4:9;
    3259 = 29*112 + 11; hence not 29 divides 3259 by NAT_4:9;
    3259 = 31*105 + 4; hence not 31 divides 3259 by NAT_4:9;
    3259 = 37*88 + 3; hence not 37 divides 3259 by NAT_4:9;
    3259 = 41*79 + 20; hence not 41 divides 3259 by NAT_4:9;
    3259 = 43*75 + 34; hence not 43 divides 3259 by NAT_4:9;
    3259 = 47*69 + 16; hence not 47 divides 3259 by NAT_4:9;
    3259 = 53*61 + 26; hence not 53 divides 3259 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3259 & n is prime
  holds not n divides 3259 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
