
theorem
  4271 is prime
proof
  now
    4271 = 2*2135 + 1; hence not 2 divides 4271 by NAT_4:9;
    4271 = 3*1423 + 2; hence not 3 divides 4271 by NAT_4:9;
    4271 = 5*854 + 1; hence not 5 divides 4271 by NAT_4:9;
    4271 = 7*610 + 1; hence not 7 divides 4271 by NAT_4:9;
    4271 = 11*388 + 3; hence not 11 divides 4271 by NAT_4:9;
    4271 = 13*328 + 7; hence not 13 divides 4271 by NAT_4:9;
    4271 = 17*251 + 4; hence not 17 divides 4271 by NAT_4:9;
    4271 = 19*224 + 15; hence not 19 divides 4271 by NAT_4:9;
    4271 = 23*185 + 16; hence not 23 divides 4271 by NAT_4:9;
    4271 = 29*147 + 8; hence not 29 divides 4271 by NAT_4:9;
    4271 = 31*137 + 24; hence not 31 divides 4271 by NAT_4:9;
    4271 = 37*115 + 16; hence not 37 divides 4271 by NAT_4:9;
    4271 = 41*104 + 7; hence not 41 divides 4271 by NAT_4:9;
    4271 = 43*99 + 14; hence not 43 divides 4271 by NAT_4:9;
    4271 = 47*90 + 41; hence not 47 divides 4271 by NAT_4:9;
    4271 = 53*80 + 31; hence not 53 divides 4271 by NAT_4:9;
    4271 = 59*72 + 23; hence not 59 divides 4271 by NAT_4:9;
    4271 = 61*70 + 1; hence not 61 divides 4271 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4271 & n is prime
  holds not n divides 4271 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
