
theorem
  4297 is prime
proof
  now
    4297 = 2*2148 + 1; hence not 2 divides 4297 by NAT_4:9;
    4297 = 3*1432 + 1; hence not 3 divides 4297 by NAT_4:9;
    4297 = 5*859 + 2; hence not 5 divides 4297 by NAT_4:9;
    4297 = 7*613 + 6; hence not 7 divides 4297 by NAT_4:9;
    4297 = 11*390 + 7; hence not 11 divides 4297 by NAT_4:9;
    4297 = 13*330 + 7; hence not 13 divides 4297 by NAT_4:9;
    4297 = 17*252 + 13; hence not 17 divides 4297 by NAT_4:9;
    4297 = 19*226 + 3; hence not 19 divides 4297 by NAT_4:9;
    4297 = 23*186 + 19; hence not 23 divides 4297 by NAT_4:9;
    4297 = 29*148 + 5; hence not 29 divides 4297 by NAT_4:9;
    4297 = 31*138 + 19; hence not 31 divides 4297 by NAT_4:9;
    4297 = 37*116 + 5; hence not 37 divides 4297 by NAT_4:9;
    4297 = 41*104 + 33; hence not 41 divides 4297 by NAT_4:9;
    4297 = 43*99 + 40; hence not 43 divides 4297 by NAT_4:9;
    4297 = 47*91 + 20; hence not 47 divides 4297 by NAT_4:9;
    4297 = 53*81 + 4; hence not 53 divides 4297 by NAT_4:9;
    4297 = 59*72 + 49; hence not 59 divides 4297 by NAT_4:9;
    4297 = 61*70 + 27; hence not 61 divides 4297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4297 & n is prime
  holds not n divides 4297 by XPRIMET1:36;
  hence thesis by NAT_4:14;
end;
