
theorem
  4603 is prime
proof
  now
    4603 = 2*2301 + 1; hence not 2 divides 4603 by NAT_4:9;
    4603 = 3*1534 + 1; hence not 3 divides 4603 by NAT_4:9;
    4603 = 5*920 + 3; hence not 5 divides 4603 by NAT_4:9;
    4603 = 7*657 + 4; hence not 7 divides 4603 by NAT_4:9;
    4603 = 11*418 + 5; hence not 11 divides 4603 by NAT_4:9;
    4603 = 13*354 + 1; hence not 13 divides 4603 by NAT_4:9;
    4603 = 17*270 + 13; hence not 17 divides 4603 by NAT_4:9;
    4603 = 19*242 + 5; hence not 19 divides 4603 by NAT_4:9;
    4603 = 23*200 + 3; hence not 23 divides 4603 by NAT_4:9;
    4603 = 29*158 + 21; hence not 29 divides 4603 by NAT_4:9;
    4603 = 31*148 + 15; hence not 31 divides 4603 by NAT_4:9;
    4603 = 37*124 + 15; hence not 37 divides 4603 by NAT_4:9;
    4603 = 41*112 + 11; hence not 41 divides 4603 by NAT_4:9;
    4603 = 43*107 + 2; hence not 43 divides 4603 by NAT_4:9;
    4603 = 47*97 + 44; hence not 47 divides 4603 by NAT_4:9;
    4603 = 53*86 + 45; hence not 53 divides 4603 by NAT_4:9;
    4603 = 59*78 + 1; hence not 59 divides 4603 by NAT_4:9;
    4603 = 61*75 + 28; hence not 61 divides 4603 by NAT_4:9;
    4603 = 67*68 + 47; hence not 67 divides 4603 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4603 & n is prime
  holds not n divides 4603 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
