
theorem
  6217 is prime
proof
  now
    6217 = 2*3108 + 1; hence not 2 divides 6217 by NAT_4:9;
    6217 = 3*2072 + 1; hence not 3 divides 6217 by NAT_4:9;
    6217 = 5*1243 + 2; hence not 5 divides 6217 by NAT_4:9;
    6217 = 7*888 + 1; hence not 7 divides 6217 by NAT_4:9;
    6217 = 11*565 + 2; hence not 11 divides 6217 by NAT_4:9;
    6217 = 13*478 + 3; hence not 13 divides 6217 by NAT_4:9;
    6217 = 17*365 + 12; hence not 17 divides 6217 by NAT_4:9;
    6217 = 19*327 + 4; hence not 19 divides 6217 by NAT_4:9;
    6217 = 23*270 + 7; hence not 23 divides 6217 by NAT_4:9;
    6217 = 29*214 + 11; hence not 29 divides 6217 by NAT_4:9;
    6217 = 31*200 + 17; hence not 31 divides 6217 by NAT_4:9;
    6217 = 37*168 + 1; hence not 37 divides 6217 by NAT_4:9;
    6217 = 41*151 + 26; hence not 41 divides 6217 by NAT_4:9;
    6217 = 43*144 + 25; hence not 43 divides 6217 by NAT_4:9;
    6217 = 47*132 + 13; hence not 47 divides 6217 by NAT_4:9;
    6217 = 53*117 + 16; hence not 53 divides 6217 by NAT_4:9;
    6217 = 59*105 + 22; hence not 59 divides 6217 by NAT_4:9;
    6217 = 61*101 + 56; hence not 61 divides 6217 by NAT_4:9;
    6217 = 67*92 + 53; hence not 67 divides 6217 by NAT_4:9;
    6217 = 71*87 + 40; hence not 71 divides 6217 by NAT_4:9;
    6217 = 73*85 + 12; hence not 73 divides 6217 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 6217 & n is prime
  holds not n divides 6217 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
