
theorem
  7621 is prime
proof
  now
    7621 = 2*3810 + 1; hence not 2 divides 7621 by NAT_4:9;
    7621 = 3*2540 + 1; hence not 3 divides 7621 by NAT_4:9;
    7621 = 5*1524 + 1; hence not 5 divides 7621 by NAT_4:9;
    7621 = 7*1088 + 5; hence not 7 divides 7621 by NAT_4:9;
    7621 = 11*692 + 9; hence not 11 divides 7621 by NAT_4:9;
    7621 = 13*586 + 3; hence not 13 divides 7621 by NAT_4:9;
    7621 = 17*448 + 5; hence not 17 divides 7621 by NAT_4:9;
    7621 = 19*401 + 2; hence not 19 divides 7621 by NAT_4:9;
    7621 = 23*331 + 8; hence not 23 divides 7621 by NAT_4:9;
    7621 = 29*262 + 23; hence not 29 divides 7621 by NAT_4:9;
    7621 = 31*245 + 26; hence not 31 divides 7621 by NAT_4:9;
    7621 = 37*205 + 36; hence not 37 divides 7621 by NAT_4:9;
    7621 = 41*185 + 36; hence not 41 divides 7621 by NAT_4:9;
    7621 = 43*177 + 10; hence not 43 divides 7621 by NAT_4:9;
    7621 = 47*162 + 7; hence not 47 divides 7621 by NAT_4:9;
    7621 = 53*143 + 42; hence not 53 divides 7621 by NAT_4:9;
    7621 = 59*129 + 10; hence not 59 divides 7621 by NAT_4:9;
    7621 = 61*124 + 57; hence not 61 divides 7621 by NAT_4:9;
    7621 = 67*113 + 50; hence not 67 divides 7621 by NAT_4:9;
    7621 = 71*107 + 24; hence not 71 divides 7621 by NAT_4:9;
    7621 = 73*104 + 29; hence not 73 divides 7621 by NAT_4:9;
    7621 = 79*96 + 37; hence not 79 divides 7621 by NAT_4:9;
    7621 = 83*91 + 68; hence not 83 divides 7621 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 7621 & n is prime
  holds not n divides 7621 by XPRIMET1:46;
  hence thesis by NAT_4:14;
end;
