
theorem
  4597 is prime
proof
  now
    4597 = 2*2298 + 1; hence not 2 divides 4597 by NAT_4:9;
    4597 = 3*1532 + 1; hence not 3 divides 4597 by NAT_4:9;
    4597 = 5*919 + 2; hence not 5 divides 4597 by NAT_4:9;
    4597 = 7*656 + 5; hence not 7 divides 4597 by NAT_4:9;
    4597 = 11*417 + 10; hence not 11 divides 4597 by NAT_4:9;
    4597 = 13*353 + 8; hence not 13 divides 4597 by NAT_4:9;
    4597 = 17*270 + 7; hence not 17 divides 4597 by NAT_4:9;
    4597 = 19*241 + 18; hence not 19 divides 4597 by NAT_4:9;
    4597 = 23*199 + 20; hence not 23 divides 4597 by NAT_4:9;
    4597 = 29*158 + 15; hence not 29 divides 4597 by NAT_4:9;
    4597 = 31*148 + 9; hence not 31 divides 4597 by NAT_4:9;
    4597 = 37*124 + 9; hence not 37 divides 4597 by NAT_4:9;
    4597 = 41*112 + 5; hence not 41 divides 4597 by NAT_4:9;
    4597 = 43*106 + 39; hence not 43 divides 4597 by NAT_4:9;
    4597 = 47*97 + 38; hence not 47 divides 4597 by NAT_4:9;
    4597 = 53*86 + 39; hence not 53 divides 4597 by NAT_4:9;
    4597 = 59*77 + 54; hence not 59 divides 4597 by NAT_4:9;
    4597 = 61*75 + 22; hence not 61 divides 4597 by NAT_4:9;
    4597 = 67*68 + 41; hence not 67 divides 4597 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4597 & n is prime
  holds not n divides 4597 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
