
theorem
  4621 is prime
proof
  now
    4621 = 2*2310 + 1; hence not 2 divides 4621 by NAT_4:9;
    4621 = 3*1540 + 1; hence not 3 divides 4621 by NAT_4:9;
    4621 = 5*924 + 1; hence not 5 divides 4621 by NAT_4:9;
    4621 = 7*660 + 1; hence not 7 divides 4621 by NAT_4:9;
    4621 = 11*420 + 1; hence not 11 divides 4621 by NAT_4:9;
    4621 = 13*355 + 6; hence not 13 divides 4621 by NAT_4:9;
    4621 = 17*271 + 14; hence not 17 divides 4621 by NAT_4:9;
    4621 = 19*243 + 4; hence not 19 divides 4621 by NAT_4:9;
    4621 = 23*200 + 21; hence not 23 divides 4621 by NAT_4:9;
    4621 = 29*159 + 10; hence not 29 divides 4621 by NAT_4:9;
    4621 = 31*149 + 2; hence not 31 divides 4621 by NAT_4:9;
    4621 = 37*124 + 33; hence not 37 divides 4621 by NAT_4:9;
    4621 = 41*112 + 29; hence not 41 divides 4621 by NAT_4:9;
    4621 = 43*107 + 20; hence not 43 divides 4621 by NAT_4:9;
    4621 = 47*98 + 15; hence not 47 divides 4621 by NAT_4:9;
    4621 = 53*87 + 10; hence not 53 divides 4621 by NAT_4:9;
    4621 = 59*78 + 19; hence not 59 divides 4621 by NAT_4:9;
    4621 = 61*75 + 46; hence not 61 divides 4621 by NAT_4:9;
    4621 = 67*68 + 65; hence not 67 divides 4621 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 4621 & n is prime
  holds not n divides 4621 by XPRIMET1:38;
  hence thesis by NAT_4:14;
end;
