
theorem
  3299 is prime
proof
  now
    3299 = 2*1649 + 1; hence not 2 divides 3299 by NAT_4:9;
    3299 = 3*1099 + 2; hence not 3 divides 3299 by NAT_4:9;
    3299 = 5*659 + 4; hence not 5 divides 3299 by NAT_4:9;
    3299 = 7*471 + 2; hence not 7 divides 3299 by NAT_4:9;
    3299 = 11*299 + 10; hence not 11 divides 3299 by NAT_4:9;
    3299 = 13*253 + 10; hence not 13 divides 3299 by NAT_4:9;
    3299 = 17*194 + 1; hence not 17 divides 3299 by NAT_4:9;
    3299 = 19*173 + 12; hence not 19 divides 3299 by NAT_4:9;
    3299 = 23*143 + 10; hence not 23 divides 3299 by NAT_4:9;
    3299 = 29*113 + 22; hence not 29 divides 3299 by NAT_4:9;
    3299 = 31*106 + 13; hence not 31 divides 3299 by NAT_4:9;
    3299 = 37*89 + 6; hence not 37 divides 3299 by NAT_4:9;
    3299 = 41*80 + 19; hence not 41 divides 3299 by NAT_4:9;
    3299 = 43*76 + 31; hence not 43 divides 3299 by NAT_4:9;
    3299 = 47*70 + 9; hence not 47 divides 3299 by NAT_4:9;
    3299 = 53*62 + 13; hence not 53 divides 3299 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3299 & n is prime
  holds not n divides 3299 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
