
theorem
  2659 is prime
proof
  now
    2659 = 2*1329 + 1; hence not 2 divides 2659 by NAT_4:9;
    2659 = 3*886 + 1; hence not 3 divides 2659 by NAT_4:9;
    2659 = 5*531 + 4; hence not 5 divides 2659 by NAT_4:9;
    2659 = 7*379 + 6; hence not 7 divides 2659 by NAT_4:9;
    2659 = 11*241 + 8; hence not 11 divides 2659 by NAT_4:9;
    2659 = 13*204 + 7; hence not 13 divides 2659 by NAT_4:9;
    2659 = 17*156 + 7; hence not 17 divides 2659 by NAT_4:9;
    2659 = 19*139 + 18; hence not 19 divides 2659 by NAT_4:9;
    2659 = 23*115 + 14; hence not 23 divides 2659 by NAT_4:9;
    2659 = 29*91 + 20; hence not 29 divides 2659 by NAT_4:9;
    2659 = 31*85 + 24; hence not 31 divides 2659 by NAT_4:9;
    2659 = 37*71 + 32; hence not 37 divides 2659 by NAT_4:9;
    2659 = 41*64 + 35; hence not 41 divides 2659 by NAT_4:9;
    2659 = 43*61 + 36; hence not 43 divides 2659 by NAT_4:9;
    2659 = 47*56 + 27; hence not 47 divides 2659 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2659 & n is prime
  holds not n divides 2659 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
