
theorem
  9619 is prime
proof
  now
    9619 = 2*4809 + 1; hence not 2 divides 9619 by NAT_4:9;
    9619 = 3*3206 + 1; hence not 3 divides 9619 by NAT_4:9;
    9619 = 5*1923 + 4; hence not 5 divides 9619 by NAT_4:9;
    9619 = 7*1374 + 1; hence not 7 divides 9619 by NAT_4:9;
    9619 = 11*874 + 5; hence not 11 divides 9619 by NAT_4:9;
    9619 = 13*739 + 12; hence not 13 divides 9619 by NAT_4:9;
    9619 = 17*565 + 14; hence not 17 divides 9619 by NAT_4:9;
    9619 = 19*506 + 5; hence not 19 divides 9619 by NAT_4:9;
    9619 = 23*418 + 5; hence not 23 divides 9619 by NAT_4:9;
    9619 = 29*331 + 20; hence not 29 divides 9619 by NAT_4:9;
    9619 = 31*310 + 9; hence not 31 divides 9619 by NAT_4:9;
    9619 = 37*259 + 36; hence not 37 divides 9619 by NAT_4:9;
    9619 = 41*234 + 25; hence not 41 divides 9619 by NAT_4:9;
    9619 = 43*223 + 30; hence not 43 divides 9619 by NAT_4:9;
    9619 = 47*204 + 31; hence not 47 divides 9619 by NAT_4:9;
    9619 = 53*181 + 26; hence not 53 divides 9619 by NAT_4:9;
    9619 = 59*163 + 2; hence not 59 divides 9619 by NAT_4:9;
    9619 = 61*157 + 42; hence not 61 divides 9619 by NAT_4:9;
    9619 = 67*143 + 38; hence not 67 divides 9619 by NAT_4:9;
    9619 = 71*135 + 34; hence not 71 divides 9619 by NAT_4:9;
    9619 = 73*131 + 56; hence not 73 divides 9619 by NAT_4:9;
    9619 = 79*121 + 60; hence not 79 divides 9619 by NAT_4:9;
    9619 = 83*115 + 74; hence not 83 divides 9619 by NAT_4:9;
    9619 = 89*108 + 7; hence not 89 divides 9619 by NAT_4:9;
    9619 = 97*99 + 16; hence not 97 divides 9619 by NAT_4:9;
  end;
  then for n being Element of NAT st 1 < n & n*n <= 9619 & n is prime
  holds not n divides 9619 by XPRIMET1:50;
  hence thesis by NAT_4:14;
end;
