
theorem
  3301 is prime
proof
  now
    3301 = 2*1650 + 1; hence not 2 divides 3301 by NAT_4:9;
    3301 = 3*1100 + 1; hence not 3 divides 3301 by NAT_4:9;
    3301 = 5*660 + 1; hence not 5 divides 3301 by NAT_4:9;
    3301 = 7*471 + 4; hence not 7 divides 3301 by NAT_4:9;
    3301 = 11*300 + 1; hence not 11 divides 3301 by NAT_4:9;
    3301 = 13*253 + 12; hence not 13 divides 3301 by NAT_4:9;
    3301 = 17*194 + 3; hence not 17 divides 3301 by NAT_4:9;
    3301 = 19*173 + 14; hence not 19 divides 3301 by NAT_4:9;
    3301 = 23*143 + 12; hence not 23 divides 3301 by NAT_4:9;
    3301 = 29*113 + 24; hence not 29 divides 3301 by NAT_4:9;
    3301 = 31*106 + 15; hence not 31 divides 3301 by NAT_4:9;
    3301 = 37*89 + 8; hence not 37 divides 3301 by NAT_4:9;
    3301 = 41*80 + 21; hence not 41 divides 3301 by NAT_4:9;
    3301 = 43*76 + 33; hence not 43 divides 3301 by NAT_4:9;
    3301 = 47*70 + 11; hence not 47 divides 3301 by NAT_4:9;
    3301 = 53*62 + 15; hence not 53 divides 3301 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 3301 & n is prime
  holds not n divides 3301 by XPRIMET1:32;
  hence thesis by NAT_4:14;
end;
