
theorem
  2663 is prime
proof
  now
    2663 = 2*1331 + 1; hence not 2 divides 2663 by NAT_4:9;
    2663 = 3*887 + 2; hence not 3 divides 2663 by NAT_4:9;
    2663 = 5*532 + 3; hence not 5 divides 2663 by NAT_4:9;
    2663 = 7*380 + 3; hence not 7 divides 2663 by NAT_4:9;
    2663 = 11*242 + 1; hence not 11 divides 2663 by NAT_4:9;
    2663 = 13*204 + 11; hence not 13 divides 2663 by NAT_4:9;
    2663 = 17*156 + 11; hence not 17 divides 2663 by NAT_4:9;
    2663 = 19*140 + 3; hence not 19 divides 2663 by NAT_4:9;
    2663 = 23*115 + 18; hence not 23 divides 2663 by NAT_4:9;
    2663 = 29*91 + 24; hence not 29 divides 2663 by NAT_4:9;
    2663 = 31*85 + 28; hence not 31 divides 2663 by NAT_4:9;
    2663 = 37*71 + 36; hence not 37 divides 2663 by NAT_4:9;
    2663 = 41*64 + 39; hence not 41 divides 2663 by NAT_4:9;
    2663 = 43*61 + 40; hence not 43 divides 2663 by NAT_4:9;
    2663 = 47*56 + 31; hence not 47 divides 2663 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 2663 & n is prime
  holds not n divides 2663 by XPRIMET1:30;
  hence thesis by NAT_4:14;
end;
