
theorem
  4639 is prime
proof
  now
    4639 = 2*2319 + 1; hence not 2 divides 4639 by NAT_4:9;
    4639 = 3*1546 + 1; hence not 3 divides 4639 by NAT_4:9;
    4639 = 5*927 + 4; hence not 5 divides 4639 by NAT_4:9;
    4639 = 7*662 + 5; hence not 7 divides 4639 by NAT_4:9;
    4639 = 11*421 + 8; hence not 11 divides 4639 by NAT_4:9;
    4639 = 13*356 + 11; hence not 13 divides 4639 by NAT_4:9;
    4639 = 17*272 + 15; hence not 17 divides 4639 by NAT_4:9;
    4639 = 19*244 + 3; hence not 19 divides 4639 by NAT_4:9;
    4639 = 23*201 + 16; hence not 23 divides 4639 by NAT_4:9;
    4639 = 29*159 + 28; hence not 29 divides 4639 by NAT_4:9;
    4639 = 31*149 + 20; hence not 31 divides 4639 by NAT_4:9;
    4639 = 37*125 + 14; hence not 37 divides 4639 by NAT_4:9;
    4639 = 41*113 + 6; hence not 41 divides 4639 by NAT_4:9;
    4639 = 43*107 + 38; hence not 43 divides 4639 by NAT_4:9;
    4639 = 47*98 + 33; hence not 47 divides 4639 by NAT_4:9;
    4639 = 53*87 + 28; hence not 53 divides 4639 by NAT_4:9;
    4639 = 59*78 + 37; hence not 59 divides 4639 by NAT_4:9;
    4639 = 61*76 + 3; hence not 61 divides 4639 by NAT_4:9;
    4639 = 67*69 + 16; hence not 67 divides 4639 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4639 & n is prime
  holds not n divides 4639 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
