
theorem
  5171 is prime
proof
  now
    5171 = 2*2585 + 1; hence not 2 divides 5171 by NAT_4:9;
    5171 = 3*1723 + 2; hence not 3 divides 5171 by NAT_4:9;
    5171 = 5*1034 + 1; hence not 5 divides 5171 by NAT_4:9;
    5171 = 7*738 + 5; hence not 7 divides 5171 by NAT_4:9;
    5171 = 11*470 + 1; hence not 11 divides 5171 by NAT_4:9;
    5171 = 13*397 + 10; hence not 13 divides 5171 by NAT_4:9;
    5171 = 17*304 + 3; hence not 17 divides 5171 by NAT_4:9;
    5171 = 19*272 + 3; hence not 19 divides 5171 by NAT_4:9;
    5171 = 23*224 + 19; hence not 23 divides 5171 by NAT_4:9;
    5171 = 29*178 + 9; hence not 29 divides 5171 by NAT_4:9;
    5171 = 31*166 + 25; hence not 31 divides 5171 by NAT_4:9;
    5171 = 37*139 + 28; hence not 37 divides 5171 by NAT_4:9;
    5171 = 41*126 + 5; hence not 41 divides 5171 by NAT_4:9;
    5171 = 43*120 + 11; hence not 43 divides 5171 by NAT_4:9;
    5171 = 47*110 + 1; hence not 47 divides 5171 by NAT_4:9;
    5171 = 53*97 + 30; hence not 53 divides 5171 by NAT_4:9;
    5171 = 59*87 + 38; hence not 59 divides 5171 by NAT_4:9;
    5171 = 61*84 + 47; hence not 61 divides 5171 by NAT_4:9;
    5171 = 67*77 + 12; hence not 67 divides 5171 by NAT_4:9;
    5171 = 71*72 + 59; hence not 71 divides 5171 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5171 & n is prime
  holds not n divides 5171 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
