
theorem
  5471 is prime
proof
  now
    5471 = 2*2735 + 1; hence not 2 divides 5471 by NAT_4:9;
    5471 = 3*1823 + 2; hence not 3 divides 5471 by NAT_4:9;
    5471 = 5*1094 + 1; hence not 5 divides 5471 by NAT_4:9;
    5471 = 7*781 + 4; hence not 7 divides 5471 by NAT_4:9;
    5471 = 11*497 + 4; hence not 11 divides 5471 by NAT_4:9;
    5471 = 13*420 + 11; hence not 13 divides 5471 by NAT_4:9;
    5471 = 17*321 + 14; hence not 17 divides 5471 by NAT_4:9;
    5471 = 19*287 + 18; hence not 19 divides 5471 by NAT_4:9;
    5471 = 23*237 + 20; hence not 23 divides 5471 by NAT_4:9;
    5471 = 29*188 + 19; hence not 29 divides 5471 by NAT_4:9;
    5471 = 31*176 + 15; hence not 31 divides 5471 by NAT_4:9;
    5471 = 37*147 + 32; hence not 37 divides 5471 by NAT_4:9;
    5471 = 41*133 + 18; hence not 41 divides 5471 by NAT_4:9;
    5471 = 43*127 + 10; hence not 43 divides 5471 by NAT_4:9;
    5471 = 47*116 + 19; hence not 47 divides 5471 by NAT_4:9;
    5471 = 53*103 + 12; hence not 53 divides 5471 by NAT_4:9;
    5471 = 59*92 + 43; hence not 59 divides 5471 by NAT_4:9;
    5471 = 61*89 + 42; hence not 61 divides 5471 by NAT_4:9;
    5471 = 67*81 + 44; hence not 67 divides 5471 by NAT_4:9;
    5471 = 71*77 + 4; hence not 71 divides 5471 by NAT_4:9;
    5471 = 73*74 + 69; hence not 73 divides 5471 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5471 & n is prime
  holds not n divides 5471 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
