
theorem
  4801 is prime
proof
  now
    4801 = 2*2400 + 1; hence not 2 divides 4801 by NAT_4:9;
    4801 = 3*1600 + 1; hence not 3 divides 4801 by NAT_4:9;
    4801 = 5*960 + 1; hence not 5 divides 4801 by NAT_4:9;
    4801 = 7*685 + 6; hence not 7 divides 4801 by NAT_4:9;
    4801 = 11*436 + 5; hence not 11 divides 4801 by NAT_4:9;
    4801 = 13*369 + 4; hence not 13 divides 4801 by NAT_4:9;
    4801 = 17*282 + 7; hence not 17 divides 4801 by NAT_4:9;
    4801 = 19*252 + 13; hence not 19 divides 4801 by NAT_4:9;
    4801 = 23*208 + 17; hence not 23 divides 4801 by NAT_4:9;
    4801 = 29*165 + 16; hence not 29 divides 4801 by NAT_4:9;
    4801 = 31*154 + 27; hence not 31 divides 4801 by NAT_4:9;
    4801 = 37*129 + 28; hence not 37 divides 4801 by NAT_4:9;
    4801 = 41*117 + 4; hence not 41 divides 4801 by NAT_4:9;
    4801 = 43*111 + 28; hence not 43 divides 4801 by NAT_4:9;
    4801 = 47*102 + 7; hence not 47 divides 4801 by NAT_4:9;
    4801 = 53*90 + 31; hence not 53 divides 4801 by NAT_4:9;
    4801 = 59*81 + 22; hence not 59 divides 4801 by NAT_4:9;
    4801 = 61*78 + 43; hence not 61 divides 4801 by NAT_4:9;
    4801 = 67*71 + 44; hence not 67 divides 4801 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4801 & n is prime
  holds not n divides 4801 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
