
theorem
  4583 is prime
proof
  now
    4583 = 2*2291 + 1; hence not 2 divides 4583 by NAT_4:9;
    4583 = 3*1527 + 2; hence not 3 divides 4583 by NAT_4:9;
    4583 = 5*916 + 3; hence not 5 divides 4583 by NAT_4:9;
    4583 = 7*654 + 5; hence not 7 divides 4583 by NAT_4:9;
    4583 = 11*416 + 7; hence not 11 divides 4583 by NAT_4:9;
    4583 = 13*352 + 7; hence not 13 divides 4583 by NAT_4:9;
    4583 = 17*269 + 10; hence not 17 divides 4583 by NAT_4:9;
    4583 = 19*241 + 4; hence not 19 divides 4583 by NAT_4:9;
    4583 = 23*199 + 6; hence not 23 divides 4583 by NAT_4:9;
    4583 = 29*158 + 1; hence not 29 divides 4583 by NAT_4:9;
    4583 = 31*147 + 26; hence not 31 divides 4583 by NAT_4:9;
    4583 = 37*123 + 32; hence not 37 divides 4583 by NAT_4:9;
    4583 = 41*111 + 32; hence not 41 divides 4583 by NAT_4:9;
    4583 = 43*106 + 25; hence not 43 divides 4583 by NAT_4:9;
    4583 = 47*97 + 24; hence not 47 divides 4583 by NAT_4:9;
    4583 = 53*86 + 25; hence not 53 divides 4583 by NAT_4:9;
    4583 = 59*77 + 40; hence not 59 divides 4583 by NAT_4:9;
    4583 = 61*75 + 8; hence not 61 divides 4583 by NAT_4:9;
    4583 = 67*68 + 27; hence not 67 divides 4583 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4583 & n is prime
  holds not n divides 4583 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
