
theorem
  5821 is prime
proof
  now
    5821 = 2*2910 + 1; hence not 2 divides 5821 by NAT_4:9;
    5821 = 3*1940 + 1; hence not 3 divides 5821 by NAT_4:9;
    5821 = 5*1164 + 1; hence not 5 divides 5821 by NAT_4:9;
    5821 = 7*831 + 4; hence not 7 divides 5821 by NAT_4:9;
    5821 = 11*529 + 2; hence not 11 divides 5821 by NAT_4:9;
    5821 = 13*447 + 10; hence not 13 divides 5821 by NAT_4:9;
    5821 = 17*342 + 7; hence not 17 divides 5821 by NAT_4:9;
    5821 = 19*306 + 7; hence not 19 divides 5821 by NAT_4:9;
    5821 = 23*253 + 2; hence not 23 divides 5821 by NAT_4:9;
    5821 = 29*200 + 21; hence not 29 divides 5821 by NAT_4:9;
    5821 = 31*187 + 24; hence not 31 divides 5821 by NAT_4:9;
    5821 = 37*157 + 12; hence not 37 divides 5821 by NAT_4:9;
    5821 = 41*141 + 40; hence not 41 divides 5821 by NAT_4:9;
    5821 = 43*135 + 16; hence not 43 divides 5821 by NAT_4:9;
    5821 = 47*123 + 40; hence not 47 divides 5821 by NAT_4:9;
    5821 = 53*109 + 44; hence not 53 divides 5821 by NAT_4:9;
    5821 = 59*98 + 39; hence not 59 divides 5821 by NAT_4:9;
    5821 = 61*95 + 26; hence not 61 divides 5821 by NAT_4:9;
    5821 = 67*86 + 59; hence not 67 divides 5821 by NAT_4:9;
    5821 = 71*81 + 70; hence not 71 divides 5821 by NAT_4:9;
    5821 = 73*79 + 54; hence not 73 divides 5821 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 5821 & n is prime
  holds not n divides 5821 by XPRIMET1:42;
  hence thesis by NAT_4:14;
end;
