
theorem
  4591 is prime
proof
  now
    4591 = 2*2295 + 1; hence not 2 divides 4591 by NAT_4:9;
    4591 = 3*1530 + 1; hence not 3 divides 4591 by NAT_4:9;
    4591 = 5*918 + 1; hence not 5 divides 4591 by NAT_4:9;
    4591 = 7*655 + 6; hence not 7 divides 4591 by NAT_4:9;
    4591 = 11*417 + 4; hence not 11 divides 4591 by NAT_4:9;
    4591 = 13*353 + 2; hence not 13 divides 4591 by NAT_4:9;
    4591 = 17*270 + 1; hence not 17 divides 4591 by NAT_4:9;
    4591 = 19*241 + 12; hence not 19 divides 4591 by NAT_4:9;
    4591 = 23*199 + 14; hence not 23 divides 4591 by NAT_4:9;
    4591 = 29*158 + 9; hence not 29 divides 4591 by NAT_4:9;
    4591 = 31*148 + 3; hence not 31 divides 4591 by NAT_4:9;
    4591 = 37*124 + 3; hence not 37 divides 4591 by NAT_4:9;
    4591 = 41*111 + 40; hence not 41 divides 4591 by NAT_4:9;
    4591 = 43*106 + 33; hence not 43 divides 4591 by NAT_4:9;
    4591 = 47*97 + 32; hence not 47 divides 4591 by NAT_4:9;
    4591 = 53*86 + 33; hence not 53 divides 4591 by NAT_4:9;
    4591 = 59*77 + 48; hence not 59 divides 4591 by NAT_4:9;
    4591 = 61*75 + 16; hence not 61 divides 4591 by NAT_4:9;
    4591 = 67*68 + 35; hence not 67 divides 4591 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4591 & n is prime
  holds not n divides 4591 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
