
theorem
  4201 is prime
proof
  now
    4201 = 2*2100 + 1; hence not 2 divides 4201 by NAT_4:9;
    4201 = 3*1400 + 1; hence not 3 divides 4201 by NAT_4:9;
    4201 = 5*840 + 1; hence not 5 divides 4201 by NAT_4:9;
    4201 = 7*600 + 1; hence not 7 divides 4201 by NAT_4:9;
    4201 = 11*381 + 10; hence not 11 divides 4201 by NAT_4:9;
    4201 = 13*323 + 2; hence not 13 divides 4201 by NAT_4:9;
    4201 = 17*247 + 2; hence not 17 divides 4201 by NAT_4:9;
    4201 = 19*221 + 2; hence not 19 divides 4201 by NAT_4:9;
    4201 = 23*182 + 15; hence not 23 divides 4201 by NAT_4:9;
    4201 = 29*144 + 25; hence not 29 divides 4201 by NAT_4:9;
    4201 = 31*135 + 16; hence not 31 divides 4201 by NAT_4:9;
    4201 = 37*113 + 20; hence not 37 divides 4201 by NAT_4:9;
    4201 = 41*102 + 19; hence not 41 divides 4201 by NAT_4:9;
    4201 = 43*97 + 30; hence not 43 divides 4201 by NAT_4:9;
    4201 = 47*89 + 18; hence not 47 divides 4201 by NAT_4:9;
    4201 = 53*79 + 14; hence not 53 divides 4201 by NAT_4:9;
    4201 = 59*71 + 12; hence not 59 divides 4201 by NAT_4:9;
    4201 = 61*68 + 53; hence not 61 divides 4201 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4201 & n is prime
  holds not n divides 4201 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
