
theorem
  4211 is prime
proof
  now
    4211 = 2*2105 + 1; hence not 2 divides 4211 by NAT_4:9;
    4211 = 3*1403 + 2; hence not 3 divides 4211 by NAT_4:9;
    4211 = 5*842 + 1; hence not 5 divides 4211 by NAT_4:9;
    4211 = 7*601 + 4; hence not 7 divides 4211 by NAT_4:9;
    4211 = 11*382 + 9; hence not 11 divides 4211 by NAT_4:9;
    4211 = 13*323 + 12; hence not 13 divides 4211 by NAT_4:9;
    4211 = 17*247 + 12; hence not 17 divides 4211 by NAT_4:9;
    4211 = 19*221 + 12; hence not 19 divides 4211 by NAT_4:9;
    4211 = 23*183 + 2; hence not 23 divides 4211 by NAT_4:9;
    4211 = 29*145 + 6; hence not 29 divides 4211 by NAT_4:9;
    4211 = 31*135 + 26; hence not 31 divides 4211 by NAT_4:9;
    4211 = 37*113 + 30; hence not 37 divides 4211 by NAT_4:9;
    4211 = 41*102 + 29; hence not 41 divides 4211 by NAT_4:9;
    4211 = 43*97 + 40; hence not 43 divides 4211 by NAT_4:9;
    4211 = 47*89 + 28; hence not 47 divides 4211 by NAT_4:9;
    4211 = 53*79 + 24; hence not 53 divides 4211 by NAT_4:9;
    4211 = 59*71 + 22; hence not 59 divides 4211 by NAT_4:9;
    4211 = 61*69 + 2; hence not 61 divides 4211 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4211 & n is prime
  holds not n divides 4211 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
