
theorem
  5297 is prime
proof
  now
    5297 = 2*2648 + 1; hence not 2 divides 5297 by NAT_4:9;
    5297 = 3*1765 + 2; hence not 3 divides 5297 by NAT_4:9;
    5297 = 5*1059 + 2; hence not 5 divides 5297 by NAT_4:9;
    5297 = 7*756 + 5; hence not 7 divides 5297 by NAT_4:9;
    5297 = 11*481 + 6; hence not 11 divides 5297 by NAT_4:9;
    5297 = 13*407 + 6; hence not 13 divides 5297 by NAT_4:9;
    5297 = 17*311 + 10; hence not 17 divides 5297 by NAT_4:9;
    5297 = 19*278 + 15; hence not 19 divides 5297 by NAT_4:9;
    5297 = 23*230 + 7; hence not 23 divides 5297 by NAT_4:9;
    5297 = 29*182 + 19; hence not 29 divides 5297 by NAT_4:9;
    5297 = 31*170 + 27; hence not 31 divides 5297 by NAT_4:9;
    5297 = 37*143 + 6; hence not 37 divides 5297 by NAT_4:9;
    5297 = 41*129 + 8; hence not 41 divides 5297 by NAT_4:9;
    5297 = 43*123 + 8; hence not 43 divides 5297 by NAT_4:9;
    5297 = 47*112 + 33; hence not 47 divides 5297 by NAT_4:9;
    5297 = 53*99 + 50; hence not 53 divides 5297 by NAT_4:9;
    5297 = 59*89 + 46; hence not 59 divides 5297 by NAT_4:9;
    5297 = 61*86 + 51; hence not 61 divides 5297 by NAT_4:9;
    5297 = 67*79 + 4; hence not 67 divides 5297 by NAT_4:9;
    5297 = 71*74 + 43; hence not 71 divides 5297 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5297 & n is prime
  holds not n divides 5297 by XPRIMET1:40;
  hence thesis by NAT_4:14;
end;
